We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.}, author = {Giesel, Kristina and Sahlmann, Hanno}, faupublication = {yes}, journal = {PoS - Proceedings of Science}, pages = {55}, peerreviewed = {Yes}, title = {{From} {Classical} {To} {Quantum} {Gravity}: {Introduction} to {Loop} {Quantum} {Gravity}}, volume = {C11-02-28}, year = {2011} } @article{faucris.122512324, abstract = {Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantum field. In this paper, we extend that construction to more general theories which do not refer to any background, spacetime metric (and in which the space of histories does not admit a natural linear structure). Examples include certain gauge theories, topological field theories and relativistic gravitational theories. The treatment is self-contained in the sense that an a priori knowledge of the Osterwalder-Schrader theorem is not assumed.}, author = {Ashtekar, Abhay and Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {4919-4940}, peerreviewed = {Yes}, title = {{Constructing} {Hamiltonian} quantum theories from path integrals in a diffeomorphism-invariant context}, volume = {17}, year = {2000} } @article{faucris.122507264, abstract = {In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity.}, author = {Bahr, Benjamin and Thiemann, Thomas}, doi = {10.1088/0264-9381/24/8/011}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2109-2138}, peerreviewed = {Yes}, title = {{Approximating} the physical inner product of loop quantum cosmology}, volume = {24}, year = {2007} } @article{faucris.115355504, abstract = {As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism-invariant states for a scalar field. We give a very explicit formula for the scalar product on this space and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism-invariant quantities on that space and discuss in detail the ordering issues involved. On a technical level these issues bear some similarity to those encountered in full loop quantum gravity. © 2007 IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/0264-9381/24/18/003}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {4601-4615}, peerreviewed = {Yes}, title = {{Exploring} the diffeomorphism-invariant {Hilbert} space of a scalar field}, volume = {24}, year = {2007} } @article{faucris.120516264, abstract = {We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint. © 2008 IOP Publishing Ltd.}, author = {Sahlmann, Hanno and Fewster, Christopher}, doi = {10.1088/0264-9381/25/22/225015}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Phase} space quantization and loop quantum cosmology: {A} {Wigner} function for the {Bohr}-compactified real line}, volume = {25}, year = {2008} } @article{faucris.110425964, abstract = {Spin foam models are an attempt at a covariant or path integral formulation of canonical loop quantum gravity. The construction of such models usually relies on the Plebanski formulation of general relativity as a constrained BF theory and is based on the discretization of the action on a simplicial triangulation, which may be viewed as an ultraviolet regulator. The triangulation dependence can be removed by means of group field theory techniques, which allows one to sum over all triangulations. The main tasks for these models are the correct quantum implementation of the Plebanski constraints, the existence of a semiclassical sector implementing additional 'Regge-like' constraints arising from simplicial triangulations and the definition of the physical inner product of loop quantum gravity via group field theory. Here we propose a new approach to tackle these issues stemming directly from the Holst action for general relativity, which is also a proper starting point for canonical loop quantum gravity. The discretization is performed by means of a 'cubulation' of the manifold rather than a triangulation. We give a direct interpretation of the resulting spin foam model as a generating functional for the n-point functions on the physical Hilbert space at finite regulator. This paper focuses on ideas and tasks to be performed before the model can be taken seriously. However, our analysis reveals some interesting features of this model: firstly, the structure of its amplitudes differs from the standard spin foam models. Secondly, the tetrad n-point functions admit a 'Wick-like' structure. Thirdly, the restriction to simple representations does not automatically occur-unless one makes use of the time gauge, just as in the classical theory.}, author = {Baratin, Aristide and Flori, Cecilia and Thiemann, Thomas}, doi = {10.1088/1367-2630/14/10/103054}, faupublication = {yes}, journal = {New Journal of Physics}, peerreviewed = {Yes}, title = {{The} {Holst} spin foam model via cubulations}, volume = {14}, year = {2012} } @inproceedings{faucris.106209224, abstract = {I will survey the formalism and main results of loop quantum gravity [1], [2] from a mathematical perspective. Then I take a closer look at the way black hole horizons are treated in the theory, by coupling a Chern-Simons theory on the horizon to the bulk degrees of freedom [3]. I will present some recent results on a new way to solve the self-duality equation involved directly in the quantum theory [4].}, author = {Sahlmann, Hanno}, doi = {10.1142/9789814449243_0075}, faupublication = {yes}, isbn = {9789814449236}, keywords = {Black holes; Duo isomorphism; Measures on spaces of connections; Quantum gravity; TQFT}, peerreviewed = {unknown}, publisher = {World Scientific Publishing Co.}, title = {{From} groups and knots to black hole entropy - mathematical aspects of loop quantum gravity}, year = {2013} } @article{faucris.110409904, abstract = {In this paper, we investigate the properties of gauge-invariant coherent states for loop quantum gravity, for the gauge group U(1). This is done by projecting the corresponding complexifier coherent states defined by Thiemann and Winklerto the gauge- invariant Hilbert space. This being the first step toward constructing physical coherent states, we arrive at a set of gauge- invariant states that approximate well the gauge-invariant degrees of freedom of Abelian loop quantum gravity (LQG). Furthermore, these states turn out to encode explicit information about the graph topology, and show the same pleasant peakedness properties known from the gauge-variant complexifier coherent states. In a companion paper, we will turn to the more sophisticated case of SU(2).}, author = {Bahr, Benjamin and Thiemann, Thomas}, doi = {10.1088/0264-9381/26/4/045011}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Gauge}-invariant coherent states for loop quantum gravity: {I}. {Abelian} gauge groups}, volume = {26}, year = {2009} } @misc{faucris.121681384, author = {Stumpf, Henning and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Geometry} of four-valent spin networks with spin 1/2}, year = {2013} } @article{faucris.123221164, abstract = {We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far. (C) 2001 Elsevier Science B.V. All rights reserved.}, author = {Sahlmann, Hanno and Thiemann, Thomas and Winkler, Oliver}, faupublication = {no}, journal = {Nuclear Physics B}, pages = {401-440}, peerreviewed = {Yes}, title = {{Coherent} states for canonical quantum general relativity and the infinite tensor product extension}, volume = {606}, year = {2001} } @article{faucris.107360264, abstract = {The no-boundary wavefunction of quantum gravity usually assigns only very small probability to long periods of inflation. This was a reason to doubt about the no-boundary wavefunction to explain the observational universe. We study the no-boundary proposal in the context of multi-field inflation to see whether the number of fields changes the situation. For a simple model, we find that indeed the no-boundary wavefunction can give higher probability for sufficient inflation, but the number of fields involved N has to be very high, e.g., N ≃ m. © 2013 IOP Publishing Ltd.}, author = {Hwang, Dong-il and Kim, Soo A and Lee, Bum-Hoon and Sahlmann, Hanno and Yeom, Dong-han}, doi = {10.1088/0264-9381/30/16/165016}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{No}-boundary measure and preference for large e-foldings in multi-field inflation}, volume = {30}, year = {2013} } @masterthesis{faucris.110377344, author = {Alex, Nils and Giesel, Kristina}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Algebraic} {Loop} {Quantisation} of the {Gowdy} {Model}: {The} {Master} {Constraint}}, year = {2015} } @masterthesis{faucris.200383145, abstract = {The objective of this Master’s thesis is to consider the well-known framework of Weyl algebras and

quasifree states in order to find out if it is possible to apply the general ideas, coming from algebraic

quantum theory, to the theory of loop quantum gravity.

Starting from the U(1) toy-model of the canonical commutation relation of the holonomy-flux

algebra, underlying loop quantum gravity, we construct a Weyl C^{*}-algebra generated by so-called

Weyl elements that arise from combining holonomies and exponentiated electric fluxes, which are

the canonically conjugated variables of the theory. Quasifree states are a certain notion of Gaussian

states, directly emerging from Weyl algebras. Because it seems to be impossible to establish such

states on the algebra we found, we develop a different notion states that is only Gaussian in one of

the variables and hence is referred to as almost-quasifree states. For such a state, which is Gaussian

in the fluxes, we find a representation on a Hilbert space that combines the Hilbert space of loop

quantum gravity with the Fock space of a scalar field.

For the canonical commutation relation of the actual theory, which involves SU(2) Yang-Mills

holonomies and the corresponding fluxes, we try to generalize our results. It is possible to define

Weyl-like elements for holonomies along a single path and a set of exponentiated fluxes. We work

toward a notion of elements that take care of more distinct edges or even graphs. It is, however,

not clear if these also generate a C*-algebra. Without an underlying Weyl algebra we successfully

generalize the almost-quasifree representation, found for the toy-model, and analyze its properties

by re-deriving the area operator of loop quantum gravity in this new representation.

M modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra A⊆C∞(M)" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="0">A⊆C∞(M) which has to satisfy a non-degeneracy condition (the differentials of elements of A" id="MathJax-Element-2-Frame" role="presentation" style="position: relative;" tabindex="0">A separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form *κ* on a Lie algebra g" id="MathJax-Element-3-Frame" role="presentation" style="position: relative;" tabindex="0">g and a *κ*-skew-symmetric derivation *D* a weak affine Poisson structure on g" id="MathJax-Element-4-Frame" role="presentation" style="position: relative;" tabindex="0">g itself. This leads naturally to a concept of a Hamiltonian *G*-action on a weak Poisson manifold with a g" id="MathJax-Element-5-Frame" role="presentation" style="position: relative;" tabindex="0">g

-valued momentum map and hence to a generalization of quasi-hamiltonian group actions.

},
author = {Neeb, Karl-Hermann and Thiemann, Thomas and Sahlmann, Hanno},
booktitle = {Springer Proceedings in Mathematics & Statistics},
editor = {V. Dobrev},
faupublication = {yes},
isbn = {978-4-431-55284-0},
pages = {105-136},
peerreviewed = {unknown},
publisher = {Springer Japan},
title = {{Weak} {Poisson} structures on infinite dimensional manifolds and hamiltonian actions},
url = {https://arxiv.org/abs/1402.6818},
volume = {111},
year = {2015}
}
@article{faucris.122529484,
abstract = {Canonical quantization of constrained systems with first-class constraints via Dirac's operator constraint method proceeds by the theory of Rigged Hilbert spaces, sometimes also called refined algebraic quantization. This method can work when the constraints form a Lie algebra. When the constraints only close with nontrivial structure functions, the Rigging map can no longer be defined. To overcome this obstacle, the master constraint method has been proposed which replaces the individual constraints by a weighted sum of absolute squares of the constraints. Now the direct integral decomposition (DID) methods, which are closely related to Rigged Hilbert spaces, become available and have been successfully tested in various situations. It is relatively straightforward to relate the rigging inner product to the path integral that one obtains via reduced phase space methods. However, for the master constraint, this is not at all obvious. In this paper we find sufficient conditions under which such a relation can be established. Key to our analysis is the possibility to pass to equivalent, Abelian constraints, at least locally in phase space. Then the master constraint DID for those Abelian constraints can be directly related to the rigging map and therefore has a path integral formulation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3486359]},
author = {Han, Muxin and Thiemann, Thomas},
doi = {10.1063/1.3486359},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
keywords = {Dirac equation;Hilbert spaces;integral equations;Lie algebras;master equation;quantisation (quantum theory)},
peerreviewed = {Yes},
title = {{On} the relation between rigging inner product and master constraint direct integral decomposition},
volume = {51},
year = {2010}
}
@article{faucris.110404404,
abstract = {The formalism introduced in this paper is immediately applicable also to lattice gauge theory in the presence of a (Minkowski) background structure on a possibly infinite lattice.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2025-2064},
peerreviewed = {Yes},
title = {{Gauge} field theory coherent states ({GCS}): {I}. {General} properties},
volume = {18},
year = {2001}
}
@article{faucris.120515604,
abstract = {In a remarkable paper (Koslowski T A 2007 arXiv:0709.3465[gr-qc]), Koslowski introduced kinematical representations for loop quantum gravity in which a non-degenerate spatial background metric is present. He also considered their properties and showed that Gauß and diffeomorphism constraints can be implemented. With this paper, we streamline and extend his treatment. In particular, we show that the standard regularization of the geometric operators leads to well-defined operators in the new representations, and we work out their properties fully. We also give details on the implementation of the constraints. All of this is done in such a way as to show that the standard representation is a particular (and in some ways exceptional) case of the more general constructions. This does not mean that these new representations are as fundamental as the standard one. Rather, we believe they might be useful to find some form of effective theory of loop quantum gravity on large scales. © 2010 IOP Publishing Ltd.},
author = {Sahlmann, Hanno},
doi = {10.1088/0264-9381/27/22/225007},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{On} loop quantum gravity kinematics with a non-degenerate spatial background},
volume = {27},
year = {2010}
}
@article{faucris.123504524,
abstract = {In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family of gravitational scalar constraints. They preserve the Hilbert space for every choice of lapse function. Thus adjointness and commutator properties of the constraint can be investigated in a straightforward manner. We show how the space of solutions of the symmetrized constraint can be defined by spectral decomposition, and the Hilbert space of physical states by subsequently fully implementing the diffeomorphism constraint. The relationship of the solutions to those resulting from a proposal for a symmetric constraint operator by Thiemann remains to be elucidated.},
author = {Sahlmann, Hanno and Lewandowski, Jerzy},
doi = {10.1103/PhysRevD.91.044022},
faupublication = {yes},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
peerreviewed = {unknown},
title = {{Symmetric} scalar constraint for loop quantum gravity},
volume = {91},
year = {2015}
}
@article{faucris.123831664,
abstract = {In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to perform a reduced phase space quantization of the theory, thus possibly avoiding problems with the (Dirac) operator constraint quantization method for a constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrize the space of theories considered so far. We then describe the quantum theory of a model that, to the best of our knowledge, has only been considered classically so far. This model could arguably be called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian, while at the same time reducing all constraints of general relativity.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/32/13/135015},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {scalar material reference systems;loop quantum gravity;Dirac observables},
peerreviewed = {Yes},
title = {{Scalar} material reference systems and loop quantum gravity},
volume = {32},
year = {2015}
}
@article{faucris.110416504,
abstract = {Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this paper we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantization and, more specifically, with the master constraint quantization for first-class constraints. For first-class constraints with nontrivial structure functions the equivalence can only be established by passing to Abelian(ized) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second-class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.},
author = {Han, Muxin and Thiemann, Thomas},
doi = {10.1088/0264-9381/27/22/225019},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{On} the relation between operator constraint, master constraint, reduced phase space and path integral quantization},
volume = {27},
year = {2010}
}
@article{faucris.110386144,
abstract = {The space of solutions to all constraints turns out to be much larger than that obtained by traditional approaches, however, it is fully included. Thus, by a suitable restriction of the solution space, we can recover all former results which gives confidence in the new quantization methods. The meaning of the remaining 'spurious solutions' is discussed.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1249-1280},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD}): {IV}. 2+1 {Euclidean} quantum gravity as a model to test 3+1 {Lorentzian} quantum gravity},
volume = {15},
year = {1998}
}
@article{faucris.123618704,
abstract = {This new trick might also be of interest for Yang-Mills theories on curved backgrounds.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1907-1921},
peerreviewed = {Yes},
title = {{ON} {THE} {SOLUTION} {OF} {THE} {INITIAL}-{VALUE} {CONSTRAINTS} {FOR} {GENERAL}-{RELATIVITY} {COUPLED} {TO} {MATTER} {IN} {TERMS} {OF} {ASHTEKAR} {VARIABLES}},
volume = {10},
year = {1993}
}
@article{faucris.200623158,
abstract = {The theory of cosmological perturbations is a well elaborated field. To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up to the considered order in the perturbations. For linear cosmological perturbations one works with the so-called Bardeen potentials widely used in this context. However, there exists no common procedure to construct gauge invariant quantities also for higher order perturbations. Usually, one has to find new gauge invariant quantities independently for each order in perturbation theory. With the relational formalism introduced by Rovelli and further developed by Dittrich and Thiemann, it is in principle possible to calculate manifestly gauge invariant quantities, that is quantities that are gauge invariant up to arbitrary order once one has chosen a set of so-called reference fields, often also called clock fields. This article contains a review of the relational formalism and its application to canonical general relativity following the work of Garcia, Pons, Sundermeyer and Salisbury. As the starting point for our application of this formalism to cosmological perturbation theory, we also review the Hamiltonian formulation of the linearized theory for perturbations around FLRW spacetimes. The main aim of our work will be to identify clock fields in the context of the relational formalism that can be used to reconstruct quantities like the Bardeen potential as well as the Mukhanov-Sasaki variable. This requires a careful analysis of the canonical formulation in the extended ADM-phase space where lapse and shift are treated as dynamical variables. The actual construction of such observables and further investigations thereof will be carried out in our companion paper.

We derive the commutation relations of the holonomy-flux algebra in general for any dimension and gauge group. We explicitly calculate those for the case of two dimensions and one dimension. We generalize the intersection number which occurs for every commutator of holonomies and fluxes to certain equivalence classes of loops resembling homotopy classes before we start with the discussion of representations for holonomy-flux-algebras. In the case of two dimensions we discover some interesting parallels to the canonical commutation relations. We find the dual Ashtekar-Lewandowski-representation and also define the transformation rule which, just as the Fourier transformation in quantum mechanics, translates between the Ashtekar- Lewandowski-representation and its dual.

},
author = {Frembs, Markus and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{The} holonomy-flux algebra in low dimensions},
year = {2013}
}
@masterthesis{faucris.109020384,
author = {Strobel, Eckhard and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Uniform} discretizations for spherically symmetric gravity coupled to a scalar field: {A} proposal for the vacuum state},
year = {2012}
}
@inproceedings{faucris.115353964,
abstract = {As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism invariant states for a scalar field. We give a very explicit formula for the scalar product on this space, and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism invariant quantities on that space, and discuss in detail the ordering issues involved. © 2008 World Scientific Publishing Co. Pte. Ltd.},
author = {Sahlmann, Hanno},
booktitle = {11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, MG 2006},
faupublication = {no},
isbn = {9789812834263},
pages = {2791-2793},
peerreviewed = {unknown},
title = {{Exploring} the diffeomorphism invariant {Hilbert} space of a scalar field},
url = {https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84893014075&origin=inward},
venue = {Berlin},
year = {2008}
}
@misc{faucris.111478004,
author = {Eder, Konstantin and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Quantum} tetrahedron and loop quantum gravity: {The} monochromatic four-vertex},
year = {2015}
}
@misc{faucris.111490764,
author = {Reichert, Thorsten and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Angular} {Momentum} and {Quantum} {Gravity}},
year = {2010}
}
@article{faucris.123228644,
abstract = {This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein-Yang-Mills theory and 2+1 gravity. Interestingly, while Yang-Mills theory in 4D is not yet rigorously defined as ail ordinary (Wightman) quantum field theory oil Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss Constraint the master constraint can be solved explicitly, for the 2+1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by Only using spectral methods is as complicated as for 3+1 gravity and we therefore leave the complete analysis for 3+1 gravity.},
author = {Dittrich, Bianca and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/4/005},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1143-1162},
peerreviewed = {Yes},
title = {{Testing} the master constraint programme for loop quantum gravity: {V}. {Interacting} field theories},
volume = {23},
year = {2006}
}
@masterthesis{faucris.111500004,
author = {Lang, Thorsten and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Peakedness} properties of {SU}(3) heat kernel coherent states},
year = {2015}
}
@article{faucris.122540044,
abstract = {This is the third paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. In this work, we analyse models which, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper. These are systems with an SL(2, R) gauge symmetry and the complications arise because non-compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads to severe obstacles in the refined algebraic quantization programme (group averaging) and we see a trace of that in the fact that the Spectrum of the master constraint does not contain the point zero. However, the minimum of the spectrum is of order h 2 which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to h normal ordering constants). The physical Hilbert space can then be obtained after subtracting this normal ordering correction.},
author = {Thiemann, Thomas and Dittrich, Bianca},
doi = {10.1088/0264-9381/23/4/003},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1089-1120},
peerreviewed = {Yes},
title = {{Testing} the master constraint programme for loop quantum gravity: {III}. {SL}(2, {R}) models},
volume = {23},
year = {2006}
}
@article{faucris.110370964,
abstract = {This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields). Published by AIP Publishing.},
author = {Stottmeister, Alexander and Thiemann, Thomas},
doi = {10.1063/1.4954228},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Coherent} states, quantum gravity, and the {Born}-{Oppenheimer} approximation. {I}. {General} considerations},
volume = {57},
year = {2016}
}
@article{faucris.120317604,
abstract = {Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolow, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states. Published by AIP Publishing.},
author = {Lanery, Suzanne and Thiemann, Thomas},
doi = {10.1063/1.4968205},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Projective} loop quantum gravity. {I}. {State} space},
volume = {57},
year = {2016}
}
@article{faucris.123220504,
abstract = {In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G = U(1)(n) and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for R-2d are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former. Published by AIP Publishing.},
author = {Stottmeister, Alexander and Thiemann, Thomas},
doi = {10.1063/1.4954803},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Coherent} states, quantum gravity, and the {Born}-{Oppenheimer} approximation. {II}. {Compact} {Lie} groups},
volume = {57},
year = {2016}
}
@article{faucris.108873424,
abstract = {In this paper and the companion paper (Sahlmann and Thiemann 2006 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Class. Quantum Grav. 23 909), we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full-fledged quantum general relativity (QGR), starting from first principles. We stress that we do not claim to have a satisfactory answer to this question, rather our intention is to ignite a discussion by displaying the problems that have to be solved when carrying out such a programme. In the first paper of this series of two, we propose a general scheme of logical steps that one has to take in order to arrive at such a limit. We discuss the technical and conceptual problems that arise in doing so and how they can be solved in principle. As to be expected, completely new issues arise due to the fact that QGR is a background-independent theory. For instance, fundamentally the notion of a photon involves not only the Maxwell quantum field but also the metric operator - in a sense, there is no photon vacuum state but a 'photon vacuum operator'! Such problems have, to the best of our knowledge, not been discussed in the literature before, we are facing squarely one aspect of the deep conceptual difference between a background-dependent and a background-free theory. While in this first paper we focus on conceptual and abstract aspects, for instance the definition of (fundamental) n-particle states (e.g. photons), in the second paper we perform detailed calculations including, among other things, coherent state expectation values and propagation on random lattices. These calculations serve as an illustration of how far one can get with present mathematical techniques. Although they result in detailed predictions for the size of first quantum corrections such as the γ-ray burst effect, these predictions should not be taken too seriously because (a) the calculations are carried out at the kinematical level only and (b) while we can classify the amount of freedom in our constructions, the analysis of the physical significance of possible choices has just begun. © 2006 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/3/019},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {867-908},
peerreviewed = {Yes},
title = {{Towards} the {QFT} on curved spacetime limit of {QGR}: {I}. {A} general scheme},
volume = {23},
year = {2006}
}
@article{faucris.110382404,
abstract = {The present first paper aims at clarifying the classical structures that underlies this formalism, namely projective limits of symplectic manifolds [27, subsection 2.1]. In particular, this allows us to discuss accurately the issues hindering an easy implementation of the dynamics in this context, and to formulate a strategy for overcoming them [27, subsection 4.1]. (C) 2016 Elsevier B.V. All rights reserved.},
author = {Lanery, Suzanne and Thiemann, Thomas},
doi = {10.1016/j.geomphys.2016.10.010},
faupublication = {yes},
journal = {Journal of Geometry and Physics},
keywords = {Field theory;Projective limits;Symplectic geometry;Algebras of observables;Constrained Hamiltonian systems},
month = {Jan},
pages = {6-39},
peerreviewed = {Yes},
title = {{Projective} limits of state spaces {I}. {Classical} formalism},
volume = {111},
year = {2017}
}
@article{faucris.122538724,
abstract = {Recently, the master constraint programme for loop quantum gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler-DeWitt constraint equations in terms of a single master equation. While the proposal has some promising abstract features, it was until now barely tested in known models. In this series of five papers we fill this gap, thereby adding confidence to the proposal. We consider a wide range of models with increasingly more complicated constraint algebras, beginning with a finite-dimensional, Abelian algebra of constraint operators which are linear in the momenta and ending with an infinite-dimensional, non-Abelian algebra of constraint operators which closes with structure functions only and which are not even polynomial in the momenta. In all these models, we apply the master constraint programme successfully; however, the full flexibility of the method must be exploited in order to complete our task. This shows that the master constraint programme has a wide range of applicability but that there are many, physically interesting Subtleties that must be taken care of in doing so. In particular, as we will see, that we can possibly construct a master constraint operator for a nonlinear, that is, interacting quantum field theory underlines the strength of the background-independent formulation of LQG. In this first paper, we prepare the analysis of our test models by outlining the general framework of the master constraint programme. The models themselves will be studied in the remaining four papers. As a side result, we develop the direct integral decomposition (DID) programme for solving quantum constraints as an alternative to refined algebraic quantization (RAQ).},
author = {Dittrich, Bianca and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/4/001},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1025-1065},
peerreviewed = {Yes},
title = {{Testing} the master constraint programme for loop quantum gravity: {I}. {General} framework},
volume = {23},
year = {2006}
}
@article{faucris.123222264,
abstract = {Most of the fermionic part of this work is independent of the recent preprint by Baez and Krasnov and earlier work by Rovelli and Morales-Tecotl because we use new canonical fermionic variables, so-called Grassman-valued half-densities, which enable us to solve the difficult fermionic adjointness relations.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1487-1512},
peerreviewed = {Yes},
title = {{Kinematical} {Hilbert} spaces for fermionic and {Higgs} quantum field theories},
volume = {15},
year = {1998}
}
@article{faucris.224172763,
abstract = {Spin foam models (SFMs) are covariant formulations of loop quantum gravity (LQG) in four dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying the Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity can arise as a low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter delta becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.},
author = {Han, Muxin and Huang, Zichang and Zipfel, Antonia},
doi = {10.1103/PhysRevD.100.024060},
faupublication = {yes},
journal = {Physical Review D},
note = {CRIS-Team WoS Importer:2019-08-09},
peerreviewed = {Yes},
title = {{Emergent} four-dimensional linearized gravity from a spin foam model},
volume = {100},
year = {2019}
}
@article{faucris.110381744,
abstract = {In a seminal paper, Kaminski et al for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical formulation of loop quantum gravity whose Hilbert space contains all these graphs. This makes it finally possible to investigate the question whether any of the presently considered spin foam models yields a rigging map for any of the presently defined Hamiltonian constraint operators. We postulate a rigging map by summing over all abstract spin foams with arbitrary but given boundary graphs. The states induced on the boundary of these spin foams can then be identified with elements in the gauge invariant Hilbert space H-0 of the canonical theory. Of course, such a sum over all spin foams is potentially divergent and requires a regularization. Such a regularization can be obtained by introducing specific cut-offs and a weight for every single foam. Such a weight could be for example derived from a generalized formal group field theory allowing for arbitrary interaction terms. Since such a derivation is, however, technical involved we forgo to present a strict derivation and assume that there exist a weight satisfying certain natural axioms, most importantly a gluing property. These axioms are motivated by the requirement that spin foam amplitudes should define a rigging map ( physical inner product) induced by the Hamiltonian constraint. In the analysis of the resulting object we are able to identify an elementary spin foam transfer matrix that allows to generate any finite foam as a finite power of the transfer matrix. It transpires that the sum over spin foams, as written, does not define a projector on the physical Hilbert space. This statement is independent of the concrete spin foam model and Hamiltonian constraint. However, the transfer matrix potentially contains the necessary ingredient in order to construct a proper rigging map in terms of a modified transfer matrix.},
author = {Thiemann, Thomas and Zipfel, Antonia},
doi = {10.1088/0264-9381/31/12/125008},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {loop quantum gravity;spin foam;Hamiltonian constraint;rigging map},
peerreviewed = {Yes},
title = {{Linking} covariant and canonical {LQG} {II}: spin foam projector},
volume = {31},
year = {2014}
}
@masterthesis{faucris.112636744,
author = {Leitherer, Andreas and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{The} {Schrödinger} {Equation} of the {Gowdy} {Model} in {Reduced} {Algebraic} {Quantum} {Gravity}},
year = {2017}
}
@misc{faucris.214358865,
author = {Matas, Bystrik and Giesel, Kristina and Kobler, Michael},
faupublication = {yes},
peerreviewed = {automatic},
title = {{The} {Lewis}-{Riesenfeld} {Invariant} in the context of a {Loop} {Quantum} {Cosmology} quantisation},
year = {2018}
}
@article{faucris.110412544,
abstract = {Barbero has generalized the Ashtekar canonical transformation to a one-parameter scale transformation U(gamma) on the phase space of general relativity. Immirzi has noticed that in loop quantum gravity this transformation alters the spectra of geometrical quantities. We show that U(gamma) is a canonical transformation that cannot be implemented unitarily in quantum theory. This implies that there exists a one-parameter quantization ambiguity in quantum gravity, namely, a free parameter that enters the construction of the quantum theory. The purpose of this paper is to elucidate the origin and the role of this free parameter.},
author = {Thiemann, Thomas and Rovelli, Carlo},
faupublication = {no},
journal = {Physical Review D},
month = {Jan},
pages = {1009-1014},
peerreviewed = {unknown},
title = {{Immirzi} parameter in quantum general relativity},
volume = {57},
year = {1998}
}
@misc{faucris.201058655,
author = {Wichert, Josef and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{What} does the {Penrose} operator measure in loop quantum gravity?},
year = {2016}
}
@article{faucris.224623141,
abstract = {We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context of inflation considering a quasi-de Sitter spacetime. Our main interest lies in the question of to which extent these already well-established methods at the classical and quantum level for finitely many degrees of freedom can be generalized to field theory. As our results show, a straightforward generalization does in general not lead to a unitary operator on Fock space that implements the corresponding time-dependent canonical transformation associated with the Lewis-Riesenfeld invariant. The action of this operator can be rewritten as a time-dependent Bogoliubov transformation, where we also compare our results to already existing ones in the literature. We show that its generalization to Fock space has to be chosen appropriately in order to not violate the Shale-Stinespring condition. Furthermore, our analysis relates the Ermakov differential equation that plays the role of an auxiliary equation, whose solution is necessary to construct the Lewis-Riesenfeld invariant, as well as the corresponding time-dependent canonical transformation, to the defining differential equation for adiabatic vacua. Therefore, a given solution of the Ermakov equation directly yields a full solution of the differential equation for adiabatic vacua involving no truncation at some adiabatic order. As a consequence, we can interpret our result obtained here as a kind of non-squeezed Bunch-Davies mode, where the term non-squeezed refers to a possible residual squeezing that can be involved in the unitary operator for certain choices of the Bogoliubov map.},
author = {Fahn, Max Joseph and Giesel, Kristina and Kobler, Michael},
doi = {10.3390/universe5070170},
faupublication = {yes},
journal = {Universe},
keywords = {Adiabatic vacua; Bogoliubov transformation; Cosmological perturbation theory; Lewis-Riesenfeld invariant; Quantum cosmology},
note = {CRIS-Team Scopus Importer:2019-08-16},
peerreviewed = {Yes},
title = {{Dynamical} properties of the {Mukhanov}-{Sasaki} hamiltonian in the context of adiabatic vacua and the {Lewis}-{Riesenfeld} invariant},
volume = {5},
year = {2019}
}
@article{faucris.123228864,
abstract = {We combine (i) background-independent loop quantum gravity (LQG) quantization techniques, (ii) the mathematically rigorous framework of algebraic quantum field theory (AQFT) and (iii) the theory of integrable systems resulting in the invariant Pohlmeyer charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge, new, non-trivial solution to the representation problem. This solution exists (1) for any target space dimension, (2) for Minkowski signature of the target space, (3) without tachyons, (4) manifestly ghost free (no negative norm states), (5) without fixing a worldsheet or target space gauge, (6) without (Virasoro) anomalies (zero central charge), (7) while preserving manifest target space Poincare invariance and (8) without picking up UV divergences. The existence of this stable solution is, on one hand, exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. On the other hand, if such solutions are found, then this would prove that neither a critical dimension (D = 10, 11, 26) nor supersymmetry is a prediction of string theory. Rather, these would be features of the particular Fock representation of current string theory and hence would not be generic. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper, we treat the more complicated case of curved target spaces.},
author = {Thiemann, Thomas},
doi = {10.1088/0264-9381/23/6/007},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1923-1970},
peerreviewed = {Yes},
title = {{The} {LQG} string - loop quantum gravity quantization of string theory: {I}. {Flat} target space},
volume = {23},
year = {2006}
}
@article{faucris.221414065,
abstract = {Let V = ⊗^{N} k=1 Vk be an N-particle Hilbert space, whose individual single-particle space is the one with spin j and dimension d = 2j + 1. Let V(w) be the subspace of V with constant weight w, consisting of vectors whose total spins are w. We show that the combinatorial properties of the constant weight condition impose strong constraints on the reduced density matrices for any vector |ψ) in the constant weight subspace V(w), which limit the possibility of the entanglement structures of |ψ). Our results find applications in the overlapping quantum marginal problem, quantum error-correcting codes, and the spin-network structures in quantum gravity.},
author = {Chen, Jianxin and Han, Muxin and Li, Youning and Zeng, Bei and Zhou, Jie},
doi = {10.1016/S0034-4877(19)30049-7},
faupublication = {yes},
journal = {Reports on Mathematical Physics},
keywords = {constant weight subspace; perfect invariant tensors; reduced density matrix},
note = {CRIS-Team Scopus Importer:2019-06-28},
pages = {273-292},
peerreviewed = {Yes},
title = {{Local} {Density} {Matrices} of {Many}-{Body} {States} in the {Constant} {Weight} {Subspaces}},
volume = {83},
year = {2019}
}
@article{faucris.115368044,
abstract = {In loop quantum gravity, matter fields can have support only on the 'polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states cannot refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background-independent operator algebras and Hilbert spaces. Second, to make contact with low-energy physics, one has to relate this 'polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.},
author = {Sahlmann, Hanno and Ashtekar, Abhay and Lewandowski, Jerzy},
doi = {10.1088/0264-9381/20/1/103},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Polymer} and {Fock} representations for a scalar field},
volume = {20},
year = {2003}
}
@article{faucris.110368984,
abstract = {We show that the quantization of spherically symmetric pure gravity can be carried out completely in the framework of Ashtekar's self-dual representation. Consistent operator orderings can be given for the constraint functionals yielding two kinds of solutions for the constraint equations, corresponding classically to globally nondegenerate or degenerate metrics. The physical state functionals can be determined by quadratures and the reduced hamiltonian system possesses two degrees of freedom, one of them corresponding to the classical Schwarzschild mass squared and the canonically conjugate one representing a measure for the deviation of the nonstatic field configurations from the static Schwarzschild one. There is a natural choice for the scalar product making the two fundamental observables self-adjoint. Finally, a unitary transformation is performed in order to calculate the triad-representation of the physical state functionals and to provide for a solution of the appropriately regularized Wheeler-DeWitt equation.},
author = {Thiemann, Thomas and Kastrup, Hans},
faupublication = {no},
journal = {Nuclear Physics B},
pages = {211-258},
peerreviewed = {Yes},
title = {{CANONICAL} {QUANTIZATION} {OF} {SPHERICALLY} {SYMMETRICAL} {GRAVITY} {IN} {ASHTEKAR} {SELF}-{DUAL} {REPRESENTATION}},
volume = {399},
year = {1993}
}
@article{faucris.110422224,
abstract = {(vii) Equipped with this inner product, the construction of physical observables is straightforward.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1207-1247},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD}): {III}. {Quantum} constraint algebra and physical scalar product in quantum general relativity},
volume = {15},
year = {1998}
}
@article{faucris.119217604,
abstract = {In this paper we deliver the proofs for the claims, made in a companion paper, concerning the avoidance of cosmological curvature singularities in full loop quantum gravity (LQG).},
author = {Brunnemann, Johannes and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/5/002},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1429-1483},
peerreviewed = {Yes},
title = {{Unboundedness} of triad-like operators in loop quantum gravity},
volume = {23},
year = {2006}
}
@article{faucris.120054044,
abstract = {We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum holonomy-flux *-algebra that is invariant under residual diffeomorphisms-both when the standard algebra is used as well as when one uses the extended algebra proposed by Fleischhack. More precisely, we find that in both situations the GNS-Hilbert spaces coincide, and that in the Fleischhack case the additional algebra elements are just mapped to zero operators. In order for the residual diffeomorphisms to have a well-defined action on the quantum algebra, we have let them act on the fiducial cell as well as on the dynamical variables, thereby recovering covariance. Consistency with Ashtekar and Campilgia in the Bianchi case is also shown.},
author = {Engle, Jonathan and Hanusch, Maximilian and Thiemann, Thomas},
doi = {10.1007/s00220-017-2881-2},
faupublication = {yes},
journal = {Communications in Mathematical Physics},
pages = {231-246},
peerreviewed = {Yes},
title = {{Uniqueness} of the {Representation} in {Homogeneous} {Isotropic} {LQC}},
volume = {354},
year = {2017}
}
@article{faucris.110413644,
abstract = {Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one's disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauss, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045001},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {I}. {Hamiltonian} analysis},
volume = {30},
year = {2013}
}
@article{faucris.122535424,
abstract = {Of course, to show that the entire theory is finite requires more: one would need to know what the physical observables are, apart from the Hamiltonian constraint, and whether they are also finite. However, with the results given in this paper this question can now be answered, at least in principle.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1281-1314},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD}): {V}. {Quantum} gravity as the natural regulator of the {Hamiltonian} constraint of matter quantum field theories},
volume = {15},
year = {1998}
}
@misc{faucris.111423664,
author = {Zilker, Thomas and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Quantum} {Simplicity} {Constraints} and {Area} {Spectrum}},
year = {2010}
}
@article{faucris.122381644,
abstract = {In this work we focus on the quantum Einstein-Yang-Mills sector quantized by the methods of loop quantum gravity. We point out the improved UV behavior of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact with the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relationship of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.},
author = {Liegener, Klaus and Thiemann, Thomas},
doi = {10.1103/PhysRevD.94.024042},
faupublication = {yes},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
peerreviewed = {unknown},
title = {{Towards} the fundamental spectrum of the quantum {Yang}-{Mills} theory},
volume = {94},
year = {2016}
}
@misc{faucris.120355224,
author = {Sahlmann, Hanno and Beier, Udo},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Defects} as a model of spacetime foam - {Spinor} and vector structures on the defect},
year = {2015}
}
@article{faucris.120025884,
abstract = {We analyze implications of the microlocal spectrum/Hadamard condition for states in a (linear) quantum field theory on a globally hyperbolic spacetime M in the context of a (distributional) initial value formulation. More specifically, we work in 3+1-split M congruent to R x Sigma and give a bound, independent of the spacetime metric, on the wave front sets of the initial data for a quasi-free Hadamard state in a quantum field theory defined by a normally hyperbolic differential operator P acting in a vector bundle E ->(pi) M. This aims at a possible way to apply the concept of Hadamard states within approaches to quantum field theory/gravity relying on a Hamiltonian formulation, potentially without a (classical) background metric g. (C) 2016 AIP Publishing LLC.},
author = {Stottmeister, Alexander and Thiemann, Thomas},
doi = {10.1063/1.4940052},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{The} microlocal spectrum condition, initial value formulations, and background independence},
volume = {57},
year = {2016}
}
@masterthesis{faucris.118093844,
abstract = {This thesis is devoted to the study of the quantum theory of charged black holes in the context of loop quantum gravity, extending the model of the quantum black hole as considered so far in the literature. We therefore consider Maxwell theory coupled to gravity de ned on a spacetime manifold with internal boundary described by an isolated horizon, construct the Hamiltonian formulation of the classical system, quantize the corresponding symplectic phase space and nally go over to the computation of the black hole entropy. We consider the spherically symmetric case in the U(1) framework as well as the distorted case following the SU(2) approach. The resulting picture depends signi cantly on the choices made for the quantization and the de nition of the state counting. We show that there is a choice such that the Bekenstein-Hawking relation holds. At the end, we use the theory in order to address the question whether there is a correspondence between the highly damped quasinormal modes and the area spectra of quantum charged black holes in the framework of loop quantum gravity. },
author = {Eder, Konstantin and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Quantum} theory of charged black hole horizons},
year = {2017}
}
@article{faucris.110341924,
abstract = {Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor-valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non-equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores.},
author = {Schröder-Turk, Gerd and Kapfer, Sebastian and Breidenbach, B. and Beisbart, C. and Mecke, Klaus},
doi = {10.1111/j.1365-2818.2009.03331.x},
faupublication = {yes},
journal = {Journal of Microscopy},
keywords = {Anisotropy;integral geometry;microstructured and cellular;materials;Minkowski functionals;morphology;strain and deformation;Turing patterns},
pages = {57-74},
peerreviewed = {Yes},
title = {{Tensorial} {Minkowski} functionals and anisotropy measures for planar patterns},
volume = {238},
year = {2010}
}
@masterthesis{faucris.114753364,
author = {Winnekens, David and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Semiclassical} {Perturbation} {Theory} within {Loop} {Quantum} {Gravity}},
year = {2014}
}
@article{faucris.122018424,
abstract = {It is shown - in Ashtekar's canonical framework of General Relativity - that spherically symmetric (Schwarzschild) gravity in four-dimensional space-time constitutes a finite-dimensional completely integrable system. Canonically conjugate observables for asymptotically flat spacetimes are masses as action variables and - surprisingly - time variables as angle variables, each of which is associated with an asymptotic ''end'' of the Cauchy surfaces. The emergence of the time observable is a consequence of the Hamiltonian formulation and its subtleties concerning the slicing of space and time and is not in contradiction to Birkhoff's theorem. The results are of interest as to the concept of time in General Relativity, They can be formulated within the ADM formalism, too. Quantization of the system and the associated Schrodinger equation depend on the allowed spectrum of the masses.},
author = {Kastrup, Hans and Thiemann, Thomas},
faupublication = {no},
journal = {Nuclear Physics B},
pages = {665-686},
peerreviewed = {Yes},
title = {{SPHERICALLY} {SYMMETRICAL} {GRAVITY} {AS} {A} {COMPLETELY} {INTEGRABLE} {SYSTEM}},
volume = {425},
year = {1994}
}
@article{faucris.123506064,
abstract = {The present paper is the companion of Sahlmann and Thiemann (2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867) in which we proposed a scheme that tries to derive the quantum field theory (QFT) on curved spacetimes (CST) limit from background-independent quantum general relativity (QGR). The constructions of the companion paper make heavy use of the notion of semiclassical states for QGR. In the present paper, we employ the complexifier coherent states for QGR recently proposed by Thiemann and Winkler as semiclassical states, and thus fill the general formulae obtained in the companion paper with life. We demonstrate how one can, under some simplifying assumptions, explicitly compute expectation values of the operators relevant for the gravity-matter Hamiltonians of the companion paper in the complexifier coherent states. These expectation values give rise to effective matter Hamiltonians on the background on which the gravitational coherent state is peaked and thus induce approximate notions of n-particle states and matter propagation on fluctuating spacetimes. We display the details for the scalar and the electromagnetic field. The effective theories exhibit two types of corrections as compared to the ordinary QFT on CST. The first is due to the quantum fluctuations of the gravitational field and the second arises from the fact that background independence forces both geometry and matter to propagate on a spacetime of the form , where γ is a (random) graph. Finally, we obtain explicit numerical predictions for non-standard dispersion relations for the scalar and the electromagnetic field. They should, however, not be taken too seriously, due to the many ambiguities in our scheme, the analysis of the physical significance of which has only begun. We show, however, that one can classify these ambiguities at least in broad terms. © 2006 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/3/020},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {909-954},
peerreviewed = {Yes},
title = {{Towards} the {QFT} on curved spacetime limit of {QGR}: {II}. {A} concrete implementation},
volume = {23},
year = {2006}
}
@article{faucris.123480324,
abstract = {The construction of Dirac observables, that is, gauge-invariant objects, in general relativity is technically more complicated than in other gauge theories such as the standard model due to its more complicated gauge group which is closely related to the group of spacetime diffeomorphisms. However, the explicit and usually cumbersome expression of Dirac observables in terms of gauge noninvariant quantities is irrelevant if their Poisson algebra is sufficiently simple. Precisely that can be achieved by employing the relational formalism and a specific type of matter proposed originally by Brown and Kuchar, namely pressureless dust fields. Moreover one is able to derive a compact expression for a physical Hamiltonian that drives their physical time evolution. The resulting gauge-invariant Hamiltonian system is obtained by Higgs-ing the dust scalar fields and has an infinite number of conserved charges which force the Goldstone bosons to decouple from the evolution. In previous publications we have shown that explicitly for cosmological perturbations. In this paper we analyse the spherically symmetric sector of the theory and it turns out that the solutions are in one-to-one correspondence with the class of Lemaitre-Tolman-Bondi metrics. Therefore, the theory is capable of properly describing the whole class of gravitational experiments that rely on the assumption of spherical symmetry.},
author = {Giesel, Kristina and Tambornino, Johannes and Thiemann, Thomas},
doi = {10.1088/0264-9381/27/10/105013},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{LTB} spacetimes in terms of {Dirac} observables},
volume = {27},
year = {2010}
}
@article{faucris.123223364,
abstract = {We rederive the results of our companion paper, for matching space-time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the Palatini action contains second class constraints, by an appeal to the method of gauge unfixing, we map the second class system to an equivalent first class system which turns out to be identical to the first class constraint system obtained via the extension of the ADM phase space performed in our companion paper. Central to our analysis is again the appropriate treatment of the simplicity constraint. Remarkably, the simplicity constraint invariant extension of the Hamiltonian constraint, that is a necessary step in the gauge unfixing procedure, involves a correction term which is precisely the one found in the companion paper and which makes sure that the Hamiltonian constraint derived from the Palatini Lagrangian coincides with the ADM Hamiltonian constraint when Gauss and simplicity constraints are satisfied. We therefore have rederived our new connection formulation of general relativity from an independent starting point, thus confirming the consistency of this framework.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045002},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {II}. {Lagrangian} analysis},
volume = {30},
year = {2013}
}
@article{faucris.123480104,
abstract = {We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single master constraint operator. While AQG is inspired by loop quantum gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of general relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken. There simply is no lattice regulator that must be sent to zero.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/24/10/003},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2465-2497},
peerreviewed = {Yes},
title = {{Algebraic} quantum gravity ({AQG}): {I}. {Conceptual} setup},
volume = {24},
year = {2007}
}
@article{faucris.123570084,
abstract = {In this paper, we provide the techniques and proofs for the results presented in our companion paper concerning the consistency check on volume and triad operator quantization in loop quantum gravity.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/18/012},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {5693-5771},
peerreviewed = {Yes},
title = {{Consistency} check on volume and triad operator quantization in loop quantum gravity: {II}},
volume = {23},
year = {2006}
}
@article{faucris.108871224,
abstract = {The current understanding of the quantum origin of cosmic structure is discussed critically. We point out that in the existing treatments a transition from a symmetric quantum state to an (essentially classical) non-symmetric state is implicitly assumed, but not specified or analysed in any detail. In facing this issue, we are led to conclude that new physics is required to explain the apparent predictive power of the usual schemes. Furthermore, we show that the novel way of looking at the relevant issues opens new windows from where relevant information might be extracted regarding cosmological issues and perhaps even clues about aspects of quantum gravity. © 2006 IOP Publishing Ltd.},
author = {Perez, Alejandro and Sahlmann, Hanno and Sudarsky, Daniel},
doi = {10.1088/0264-9381/23/7/008},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2317-2354},
peerreviewed = {Yes},
title = {{On} the quantum origin of the seeds of cosmic structure},
volume = {23},
year = {2006}
}
@masterthesis{faucris.200464729,
abstract = {

The inflationary epoch at the beginning of the universe is commonly described within the frame- work of (linear) cosmological perturbation theory. The corresponding equation of motion for the gauge-invariant perturbations is the Mukhanov-Sasaki equation, which resembles a time-dependent harmonic oscillator. At first we will consider a mechanical analogue of the Mukhanov-Sasaki equa- tion and use the known Lewis-Riesenfeld invariant and the extended phase space formalism in- troduced in previous works in order to analyse the system. These techniques allow to construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one. The generators of this symplectic map can in turn be canonically quan- tised on the original part of the phase space, which is the constraint hypersurface of the extended theory, connecting to recent publications. Our further analysis leads us to a closed form of the time-evolution operator for the single-mode Mukhanov-Sasaki Hamiltonian, that is to the associ- ated Dyson series. We will analyse the characteristic properties of this time-evolution operator and discuss whether it can be extended to the full Fock space. Finally we give an outlook towards possible applications of these techniques to inflationary quantum cosmology.

In this work we present the regularisation of the Hamiltonian constraints in the context of the canonical description of general relativity (GR). We will start with the Hamiltonian formulation of GR and then introduce the Ashtekar-Barbero variables. After investigating the gauge trans- formations generated by the Hamiltonian constraints we present the holonomy-flux algebra where we also regularise the constraints. We will give a full derivation of the FLRW metric and then conclusively perform a regularisation for k=1 on spherical graphs.

Yet, an analysis of the theory suggests that in the quantum formulation the diffeomorphism in- variance of the theory seems to be broken in the sense that the constraints that generate the diffeomorphisms are only implemented weakly. Since the constraint algebra is the 1+1 dimen- sional version of the Dirac hypersurface deformation algebra of general relativity, the idea is that the physical subspace that corresponds to the kernel of the constraints are the diffeomorphism invariant states.

We therefore analyze the role of the hypersurface deformation algebra in the standard quantization of the bosonic string in further detail. It turns out that the spatial diffeomorphism constraint is anomaly-free, however, one also obtains that neither the physical states of the theory lie in the kernel of these constraints nor do they create physical states.

We analyze the action of the constraints in terms of the oscillations on the strings with an eye towards implementing spatial diffeos strongly. It turns out that the action is so complicated that we were unable to nd solutions.

Therefore, in a second part of the work we focus on a construction of a manifest diffeomorphism invariant quantization of the string in the spirit of previous work by Thiemann, i.e. the states are independent of the chosen parametrization. With the help of the Gelfand-Naimark-Segal construc- tion we obtain a Hilbert space and discuss a concrete representation that excites distinct points on the string. In the end we obtain a Fock space for a subalgebra of the mentioned representation and start a discussion of the diffeomorphism constraint and the mass within our framework.

The bosonic string also is a model for the hypersurface deformation algebra in loop quantum gravity and the issues of anomaly freeness. Thus our work might shed light on associated questions

}, author = {Wolz, Florian and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{On} spatially diffeomorphism invariant quantizations of the bosonic string}, year = {2015} } @article{faucris.123226884, abstract = {The volume operator plays a crucial role in the definition of the quantum dynamics Of loop quantum gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only if one has sufficient control over the Volume spectrum. While closed formulae for the matrix elements are currently available in the literature, these are complicated polynomials in 6j symbols which ill turn are given in terms of Racah's formula which is too complicated in order to perform even numerical calculations for the semiclassically important regime of large spins. Hence, so far Hot even numerically the spectrum could be accessed. In this paper, we demonstrate that by means of the Elliot-Biedenharn identify one can get rid of all the 6j symbols for any valence of: the gauge-invariant vertex, thus immensely reducing the computational effort. We use the resulting compact formula to study numerically the spectrum of the gauge-invariant 4-vertex. The techniques derived in this paper-could also be of use for the analysis of spin-spin interaction Hamiltonians of many-particle problems in atomic and nuclear physics.}, author = {Brunnemann, Johannes and Thiemann, Thomas}, doi = {10.1088/0264-9381/23/4/014}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {1289-1346}, peerreviewed = {Yes}, title = {{Simplification} of the spectral analysis of the volume operator in loop quantum gravity}, volume = {23}, year = {2006} } @article{faucris.120318924, abstract = {We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with each space point. We solve the classical and quantum dynamics of the model, which turns out to be governed by an SL(2,R) gauge symmetry, local in time. In classical theory, we solve the equations of motion, find an SO(2,2) algebra of Dirac observables, find the gauge transformations for the Lagrangian and canonical variables and for the Lagrange multipliers. In quantum theory, we find the physical states, the quantum observables, and the physical inner product, which is determined by the reality conditions. In addition, we construct the classical and quantum evolving constants of the system. The model illustrates how to describe physical gauge-invariant relative evolution when coordinate time evolution is a gauge. [S0556-2821(99)02014-7].}, author = {Montesinos, Merced and Rovelli, Carlo and Thiemann, Thomas}, faupublication = {no}, journal = {Physical Review D}, peerreviewed = {unknown}, title = {{SL}(2,{R}) model with two {Hamiltonian} constraints}, volume = {60}, year = {1999} } @article{faucris.120782464, abstract = {In this article, we investigate the assumption of equipartition of energy in arguments for the entropic nature of gravity. It has already been pointed out by other authors that equipartition is not valid for low temperatures. Here we additionally point out that it is similarly not valid for systems with bounded energy. Many explanations for black hole entropy suggest that the microscopic systems responsible have a finite dimensional state space, and thus finite maximum energy. Assuming this to be the case leads to drastic corrections to Newton's law for high gravitational fields, and, in particular, to a singularity in acceleration at finite radius away from a point mass. This is suggestive of the physics at the Schwarzschild radius. We show, however, that the location of the singularity scales differently. © 2011 American Physical Society.}, author = {Sahlmann, Hanno}, doi = {10.1103/PhysRevD.84.104010}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {Yes}, title = {{Energy} equipartition and minimal radius in entropic gravity}, volume = {84}, year = {2011} } @article{faucris.115349784, abstract = {We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Liealgebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups. © 2012 American Physical Society.}, author = {Sahlmann, Hanno and Thiemann, Thomas}, doi = {10.1103/PhysRevLett.108.111303}, faupublication = {yes}, journal = {Physical Review Letters}, peerreviewed = {Yes}, title = {{Chern}-simons expectation values and quantum horizons from loop quantum gravity and the duflo map}, volume = {108}, year = {2012} } @article{faucris.115356164, abstract = {We consider the model of gravity coupled to the Klein-Gordon time field. We do not deparametrize the theory using the scalar field before quantization, but quantize all degrees of freedom. Several new results for loop quantum gravity are obtained: (i) a Hilbert space for the gravity-matter system and a nonstandard representation of the scalar field thereon is constructed, (ii) a new operator for the scalar constraint of the coupled system is defined and investigated, (iii) methods for solving the constraint are developed. Commutators of the new quantum constraint operators correspond to the quantization of the Poisson bracket. This, however, poses problems for finding solutions. Hence the states we consider - and perhaps the whole setup - still needs some improvement. As a side result we describe a representation of the gravitational degrees of freedom in which the flux is diagonal. This representation is related to the BF theory vacuum of Dittrich and Geiller.}, author = {Lewandowski, Jerzy and Sahlmann, Hanno}, doi = {10.1103/PhysRevD.93.024042}, faupublication = {yes}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {unknown}, title = {{Loop} quantum gravity coupled to a scalar field}, volume = {93}, year = {2016} } @masterthesis{faucris.201058905, author = {Wichert, Josef and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{The} ideas of {Kaluza} and {Klein} in the context of loop quantum gravity}, year = {2018} } @article{faucris.123959704, abstract = {In this work we investigate the question under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of "no-go theorems" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider, play an important role in loop quantum gravity since they can be defined without recurse to a background geometry and they might also be of interest in the general context of quantization of non-Abelian gauge theories. © 2011 American Institute of Physics.}, author = {Sahlmann, Hanno}, doi = {10.1063/1.3525706}, faupublication = {no}, journal = {Journal of Mathematical Physics}, peerreviewed = {Yes}, title = {{When} do measures on the space of connections support the triad operators of loop quantum gravity?}, volume = {52}, year = {2011} } @article{faucris.217476379, abstract = {Quantum simulation promises to have wide applications in many fields where problems are hard to model with classical computers. Various quantum devices of different platforms have been built to tackle the problems in, say, quantum chemistry, condensed matter physics, and high-energy physics. Here, we report an experiment towards the simulation of quantum gravity by simulating the holographic entanglement entropy. On a six-qubit nuclear magnetic resonance quantum simulator, we demonstrate a key result of Anti-de Sitter/conformal field theory (AdS/CFT) correspondence-the Ryu-Takayanagi formula is demonstrated by measuring the relevant entanglement entropies on the perfect tensor state. The fidelity of our experimentally prepared the six-qubit state is 85.0% via full state tomography and reaches 93.7% if the signal-decay due to decoherence is taken into account. Our experiment serves as the basic module of simulating more complex tensor network states that exploring AdS/CFT correspondence. As the initial experimental attempt to study AdS/CFT via quantum information processing, our work opens up new avenues exploring quantum gravity phenomena on quantum simulators.}, author = {Li, Keren and Han, Muxin and Qu, Dongxue and Huang, Zichang and Long, Guilu and Wan, Yidun and Lu, Dawei and Zeng, Bei and Laflamme, Raymond}, doi = {10.1038/s41534-019-0145-z}, faupublication = {yes}, journal = {npj Quantum Information}, note = {CRIS-Team WoS Importer:2019-05-14}, peerreviewed = {Yes}, title = {{Measuring} holographic entanglement entropy on a quantum simulator}, volume = {5}, year = {2019} } @misc{faucris.122499124, author = {Sahlmann, Hanno and Seeger, Robert}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Geometric} properties of the {Livine}-{Speziale} coherent intertwiner}, year = {2015} } @article{faucris.217462920, abstract = {The large-j asymptotic behavior of the four-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large-j asymptotic behavior is determined by the critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are asymptotic phases, whose exponents equal the Regge action of gravity. The amplitude may also contains critical configurations corresponding to nondegenerate split signature 4-simplices and degenerate vector geometries. But vertex amplitudes containing at least one timelike and one spacelike tetrahedra only give Lorentzian 4-simplices, while the split signature or degenerate 4-simplex does not appear.}, author = {Liu, Hongguang and Han, Muxin}, doi = {10.1103/PhysRevD.99.084040}, faupublication = {yes}, journal = {Physical Review D}, note = {CRIS-Team Scopus Importer:2019-05-14}, peerreviewed = {Yes}, title = {{Asymptotic} analysis of spin foam amplitude with timelike triangles}, volume = {99}, year = {2019} } @article{faucris.110372944, abstract = {In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only a finite number of isolated intersections. This assumption implies a limitation on the diffeomorphisms invariance of the introduced structures. In this work, using the previous results of Baez and Sawin, we extend the existing results to a theory admitting all the possible piecewise-smooth finite paths and loops. In particular, we (a) characterize the spectrum of the Ashtekar-Isham configuration space, (b) introduce spin-web states, a generalization of the spin network states, (c) extend the diffeomorphism averaging to the spin-web states and derive a large class of diffeomorphism-invariant states and finally (d) extend the 3-geometry operators and the Hamiltonian operator.}, author = {Lewandowski, Jerzy and Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2299-2322}, peerreviewed = {Yes}, title = {{Diffeomorphism}-invariant quantum field theories of connections in terms of webs}, volume = {16}, year = {1999} } @article{faucris.217464944, abstract = {We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved technically by combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for the one-particle excitations in the high-field quantum paramagnet. We find that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents. In the frustrated case on the square lattice the system remains in the universality class of the nearest-neighbor model independent of the long-range nature of the interaction, while we argue that the quantum criticality for the triangular lattice is terminated by a first-order phase transition line.}, author = {Fey, Sebastian and Kapfer, Sebastian and Schmidt, Kai Phillip}, doi = {10.1103/PhysRevLett.122.017203}, faupublication = {yes}, journal = {Physical Review Letters}, month = {Jan}, note = {CRIS-Team Scopus Importer:2019-05-14}, peerreviewed = {Yes}, title = {{Quantum} {Criticality} of {Two}-{Dimensional} {Quantum} {Magnets} with {Long}-{Range} {Interactions}}, volume = {122}, year = {2019} } @misc{faucris.214360202, author = {Zwicknagel, Ernst-Albrecht and Giesel, Kristina and Liegener, Klaus}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Expectation} {Values} of {Holonomy}-{Operators} in {Cosmological} {Coherent} {States} for {Loop} {Quantum} {Gravity}}, year = {2018} } @article{faucris.110389444, abstract = {We analyze the stability under time evolution of complexitier coherent states (CCS) in one-dimensional mechanical systems. A system of coherent states is called stable if it evolves into another coherent state. It turns out that a system can only possess stable CCS if the classical evolution of thc variable z = e-14(i xc)q pound for a given complexifier C depends only on z itself and not on its complex conjugate. This condition is very restrictive in general so that only a few systems exist that obey this condition. However, it is possible to access a wider class of models that in principle may allow for stable coherent states associated with certain regions in the phase space by introducing action-angle coordinates.}, author = {Zipfel, Antonia and Thiemann, Thomas}, doi = {10.1103/PhysRevD.93.084030}, faupublication = {yes}, journal = {Physical Review D}, peerreviewed = {unknown}, title = {{Stable} coherent states}, volume = {93}, year = {2016} } @article{faucris.115364084, abstract = {Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a brief description of the main structures and results of quantum geometry, I review a new description of the quantized geometry in terms of polyhedra, new results on the volume operator, and a way to incorporate a classical background metric into the quantum description. Finally I describe a new type of exponentiated flux operator, and its application to Chern-Simons theory and black holes. © Published under licence by IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/1742-6596/360/1/012007}, faupublication = {no}, journal = {Journal of Physics : Conference Series}, peerreviewed = {No}, title = {{New} insights in quantum geometry}, volume = {360}, year = {2012} } @article{faucris.120553004, abstract = {Loop quantum cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of loop quantum gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical general relativity to spatially homogeneous situations which is then quantized by the methods of LQG. Thus, LQC is a quantum-mechanical toy model (finite number of degrees of freedom) for LQG (a genuine QFT with an infinite number of degrees of freedom) which provides important consistency checks. However, it is a non-trivial question whether the predictions of LQC are robust after switching on the inhomogeneous fluctuations present in full LQG. Two of the most spectacular findings of LQC are that: (1) the inverse scale factor is bounded from above on zero-volume eigenstates which hints at the avoidance of the local Curvature singularity and (2) the quantum Einstein equations are non-singular which hints at the avoidance of the global initial singularity. This rests on (1) a key technique developed for LQG and (2) the fact that there are no inhomogeneous excitations. We display the result of a calculation for LQG which proves that the (analogon of the) inverse scale factor, while densely defined, is not bounded from above on zero-volume eigenstates. Thus, in full LQG, if curvature singularity avoidance is realized, then not in this simple way. In fact, it turns out that the boundedness of the inverse scale factor is neither necessary nor sufficient for the curvature singularity avoidance and that non-singular evolution equations are neither necessary nor sufficient for initial singularity avoidance because none of these criteria are formulated in terms of observable quantities. After outlining what would be required, we present the results of a calculation for LQG which could be a first indication that our criteria at least for curvature singularity avoidance are satisfied in LQG.}, author = {Thiemann, Thomas and Brunnemann, Johannes}, doi = {10.1088/0264-9381/223/5/001}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {1395-1427}, peerreviewed = {Yes}, title = {{On} (cosmological) singularity avoidance in loop quantum gravity}, volume = {23}, year = {2006} } @article{faucris.110421564, abstract = {Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is designed to overcome the complications associated with the non-Lie-algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For the case of 3+1 gravity itself, so far only a positive quadratic form for the master constraint operator was derived. In this paper, we close this gap and prove that the quadratic form is closable and thus stems from a unique self-adjoint master constraint operator. The proof rests on a simple feature of the general pattern according to which Hamiltonian constraints in LQG are constructed and thus extends to arbitrary matter coupling and holds for any metric signature. With this result the existence of a physical Hilbert space for LQG is established by standard spectral analysis.}, author = {Thiemann, Thomas}, doi = {10.1088/0264-9381/23/7/003}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2249-2265}, peerreviewed = {Yes}, title = {{Quantum} spin dynamics: {VIII}. {The} master constraint}, volume = {23}, year = {2006} } @inproceedings{faucris.123218084, author = {Ashtekar, Abhay and Lewandowski, Jerzy and Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas}, faupublication = {no}, month = {Jan}, pages = {60-86}, peerreviewed = {unknown}, title = {{A} manifestly gauge-invariant approach to quantum theories of gauge fields}, year = {1995} } @article{faucris.115376844, abstract = {Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic lattice. We use this to calculate the lowest order coefficients of the dispersion relation for a specific one-dimensional model. © 2010 The American Physical Society.}, author = {Sahlmann, Hanno}, doi = {10.1103/PhysRevD.82.064018}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {Yes}, title = {{Wave} propagation on a random lattice}, volume = {82}, year = {2010} } @article{faucris.115353084, abstract = {We consider a novel derivation of the expectation values of holonomies in Chern-Simons theory, based on Stokes' Theorem and the functional properties of the Chern-Simons action. It involves replacing the connection by certain functional derivatives under the path integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity. © 2011 Elsevier B.V.}, author = {Sahlmann, Hanno and Thiemann, Thomas}, doi = {10.1016/j.geomphys.2011.02.013}, faupublication = {yes}, journal = {Journal of Geometry and Physics}, keywords = {Chern-Simons theory; Duflo map; Loop quantum gravity}, pages = {1104-1121}, peerreviewed = {Yes}, title = {{Chern}-{Simons} theory, {Stokes}' theorem, and the {Duflo} map}, volume = {61}, year = {2011} } @article{faucris.110411004, abstract = {This is the second paper concerning gauge-invariant coherent states for loop quantum gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the Abelian U(1) case encountered in the previous article (Class. Quantum Grav. 26 045011). We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss peaked in gauge- invariant quantities, as long as states are not labeled by degenerate gauge orbits, i.e. points where the gauge- invariant configuration space has singularities. In these cases the overlaps are still concentrated around these points, but the peak profile exhibits a plateau structure. This shows how the semiclassical properties of the states are influenced by the geometry of the gauge-invariant phase space.}, author = {Bahr, Benjamin and Thiemann, Thomas}, doi = {10.1088/0264-9381/26/4/045012}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Gauge}-invariant coherent states for loop quantum gravity: {II}. {Non}-{Abelian} gauge groups}, volume = {26}, year = {2009} } @article{faucris.123229744, abstract = {In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poisson-commuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11D SUGRA and 4D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the Rarita-Schwinger field. This is non-trivial because SUSY typically requires the Rarita-Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature.}, author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas}, doi = {10.1088/0264-9381/30/4/045006}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Towards} loop quantum supergravity ({LQSG}): {I}. {Rarita}-{Schwinger} sector}, volume = {30}, year = {2013} } @article{faucris.109456864, abstract = {In the two previous papers of this series we defined a new combinatorial approach to quantum gravity, algebraic quantum gravity (AQG). We showed that AQG reproduces the correct infinitesimal dynamics in the semiclassical limit, provided one incorrectly substitutes the non-Abelian group SU(2) by the Abelian group U(1)(3) in the calculations. The mere reason why that substitution was performed at all is that in the non-Abelian case the volume operator, pivotal for the definition of the dynamics, is not diagonizable by analytical methods. This, in contrast to the Abelian case, so far prohibited semiclassical computations. In this paper, we show why this unjustified substitution nevertheless reproduces the correct physical result. Namely, we introduce for the first time semiclassical perturbation theory within AQG ( and LQG) which allows us to compute expectation values of interesting operators such as the master constraint as a power series in h with error control. That is, in particular, matrix elements of fractional powers of the volume operator can be computed with extremely high precision for sufficiently large power of h in the h expansion. With this new tool, the non-Abelian calculation, although technically more involved, is then exactly analogous to the Abelian calculation, thus justifying the Abelian analysis in retrospect. The results of this paper turn AQG into a calculational discipline.}, author = {Giesel, Kristina and Thiemann, Thomas}, doi = {10.1088/0264-9381/24/10/005}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2565-2588}, peerreviewed = {Yes}, title = {{Algebraic} quantum gravity ({AQG}): {III}. {Semiclassical} perturbation theory}, volume = {24}, year = {2007} } @article{faucris.107356964, abstract = {In loop quantum gravity, states of the gravitational field turn out to be excitations over a vacuum state that is sharply peaked on a degenerate spatial geometry. While this vacuum is singled out as fundamental due to its invariance properties, it is also important to consider states that describe non-degenerate geometries. Such states have features of Bose condensate ground states. We discuss their construction for the Lie algebra as well as the Weyl algebra setting, and point out possible applications in effective field theory, Loop Quantum Cosmology, as well as further generalizations.}, author = {Sahlmann, Hanno and et al.}, author_hint = {Koslowski T., Sahlmann H.}, doi = {10.3842/SIGMA.2012.026}, faupublication = {no}, journal = {Symmetry Integrability and Geometry-Methods and Applications}, keywords = {Geometric condensate; Loop quantum gravity; Representations}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Loop} quantum gravity vacuum with nondegenerate geometry}, volume = {8}, year = {2012} } @article{faucris.109461924, abstract = {In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity (AQG), was introduced. In the framework of AQG, existing semiclassical tools can be applied to operators that encode the dynamics of AQG such as the master constraint operator. In this paper, we will analyse the semiclassical limit of the (extended) algebraic master constraint operator and show that it reproduces the correct infinitesimal generators of general relativity. Therefore, the question of whether general relativity is included in the semiclassical sector of the theory, which is still an open problem in LQG, can be significantly improved in the framework of AQG. For the calculations, we will substitute SU(2) with U(1)(3). That this substitution is justified will be demonstrated in the third paper ( Giesel and Thiemann 2006 Semiclassical perturbation theory Preprint gr-qc/0607101) of this series.}, author = {Giesel, Kristina and Thiemann, Thomas}, doi = {10.1088/0264-9381/24/10/004}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2499-2564}, peerreviewed = {Yes}, title = {{Algebraic} quantum gravity ({AQG}): {II}. {Semiclassical} analysis}, volume = {24}, year = {2007} } @article{faucris.110405724, abstract = {The text is supplemented by an appendix which contains extensive graphics in order to give a feeling for the so far unknown peakedness properties of the states constructed.}, author = {Thiemann, Thomas and Winkler, Oliver}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2561-2636}, peerreviewed = {Yes}, title = {{Gauge} field theory coherent states ({GCS}): {II}: {Peakedness} properties}, volume = {18}, year = {2001} } @article{faucris.226824067, abstract = {Kitaev's honeycomb-lattice spin-1/2 model has become a paradigmatic example for Z(2) quantum spin liquids, both gapped and gapless. Here we study the fate of these spin-liquid phases in differently stacked bilayer versions of the Kitaev model. Increasing the ratio between the interlayer Heisenberg coupling J(perpendicular to) and the intralayer Kitaev couplings K-x,K-y,K-z destroys the topological spin liquid in favor of a paramagnetic dimer phase. We study phase diagrams as a function of J(perpendicular to)/K and Kitaev coupling anisotropies using Majorana-fermion mean-field theory, and we employ different expansion techniques in the limits of small and large J(perpendicular to)/K. For strongly anisotropic Kitaev couplings, we derive effective models for the different layer stackings that we use to discuss the quantum phase transition out of the Kitaev phase. We find that the phase diagrams depend sensitively on the nature of the stacking and anisotropy strength. While in some stackings and at strong anisotropies we find a single transition between the Kitaev and dimer phases, other stackings are more involved. Most importantly, we prove the existence of two novel macrospin phases, which can be understood in terms of Ising chains that can be either coupled ferromagnetically or remain degenerate, thus realizing a classical spin liquid. In addition, our results suggest the existence of a flux phase with spontaneous interlayer coherence. We discuss prospects for experimental realizations.}, author = {Schmidt, Kai Phillip}, doi = {10.1103/PhysRevB.98.155101}, faupublication = {yes}, journal = {Physical Review B}, peerreviewed = {Yes}, title = {{Bilayer} {Kitaev} models: {Phase} diagrams and novel phases}, volume = {98}, year = {2018} } @article{faucris.110401104, abstract = {We investigate a certain distributional extension of the group of spatial diffeomorphisms in loop quantum gravity. This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category theory. These automorphisms have much larger orbits than piecewise analytic diffeomorphisms. In particular, we will show that graphs with the same combinatorics but different generalized knotting classes can be mapped into each other. We describe the automorphism-invariant Hilbert space and comment on how a combinatorial formulation of LQG might arise.}, author = {Bahr, Benjamin and Thiemann, Thomas}, doi = {10.1088/0264-9381/26/23/235022}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Automorphisms} in loop quantum gravity}, volume = {26}, year = {2009} } @masterthesis{faucris.123268464, author = {Bodendorfer, Norbert and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Canonical} {Analysis} of {Gravity} {Theories} without the {Time} {Gauge}}, year = {2009} } @article{faucris.109615264, abstract = {This is the fourth paper in Our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. We now move oil to free field theories with constraints, namely Maxwell theory and linearized gravity. Since the master constraint involves squares of constraint operator valued distributions, one has to be very careful in doing that and we will see that the full flexibility of the master constraint programme must be exploited in order to arrive at sensible results.}, author = {Dittrich, Bianca and Thiemann, Thomas}, doi = {10.1088/0264-9381/23/4/004}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {1121-1142}, peerreviewed = {Yes}, title = {{Testing} the master constraint programme for loop quantum gravity: {IV}. {Free} field theories}, volume = {23}, year = {2006} } @article{faucris.123223804, abstract = {After discussing the formalism at the classical level in a first paper (Lanery, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanery, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okolow (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanky, 2016, subsection 2.2) [1]. (C) 2017 Elsevier B.V. All rights reserved.}, author = {Lanery, Suzanne and Thiemann, Thomas}, doi = {10.1016/j.geomphys.2017.01.011}, faupublication = {yes}, journal = {Journal of Geometry and Physics}, keywords = {Quantum field theory;Projective limits;Algebras of observables;Geometric quantization;Position representation;Holomorphic quantization}, pages = {10-51}, peerreviewed = {Yes}, title = {{Projective} limits of state spaces {II}. {Quantum} formalism}, volume = {116}, year = {2017} } @book{faucris.109463244, abstract = {This volume presents a snapshot of the state-of-the-art in loop quantum gravity from the perspective of younger leading researchers. It takes the reader from the basics to recent advances, thereby bridging an important gap.

The aim is two-fold — to provide a contemporary introduction to the entire field for students and post-docs, and to present an overview of the current status for more senior researchers. The contributions include the latest developments that are not discussed in existing books, particularly recent advances in quantum dynamics both in the Hamiltonian and sum over histories approaches; and applications to cosmology of the early universe and to the quantum aspects of black holes.}, author = {Giesel, Kristina and Laddha, Alok and Varadarajan, Madhavan and Bianchi, Eugenio and Oriti, Daniele and Dittrich, Biancha and Agullo, Ivan and Singh, Parampreet and Fernando, Barbero and Perez, Alejandro and Barrau, Aurilien and Grain, Julien}, edition = {1}, editor = {Abhay A, Pullin, J}, faupublication = {yes}, isbn = {978-981-3209-92-3}, peerreviewed = {Yes}, publisher = {World Scientific}, series = {100 Years of General Relativity.}, title = {{Loop} {Quantum} {Gravity}. {The} first 30 years.}, volume = {4}, year = {2017} } @article{faucris.108871884, abstract = {In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of ground- or KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-pnt function is of Hadamard form). The fields can be of bosonic or fermionic character. We also give an abstract version of this result by showing that passive states of a topological *-dynamical system have an asymptotic pair correlation spectrum of a specific type.}, author = {Sahlmann, Hanno and Verch, Rainer}, faupublication = {no}, journal = {Communications in Mathematical Physics}, pages = {705-731}, peerreviewed = {Yes}, title = {{Passivity} and microlocal spectrum condition}, url = {https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=0034343139&origin=inward}, volume = {214}, year = {2000} } @article{faucris.107352124, abstract = {We provide a precise definition and analysis of quantum causal histories (QCHs). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. We show that this local description of evolution is sufficient and that unitary evolution can be recovered wherever it should actually be expected. This formalism may describe a quantum cosmology without an assumption of global hyperbolicity; it is thus more general than the Wheeler-De Witt approach. The structure of a QCH is also closely related to quantum information theory and algebraic quantum field theory on a causal set.}, author = {Hawkins, Eli and Markopoulou, Fotini and Sahlmann, Hanno}, doi = {10.1088/0264-9381/20/16/320}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {3839-3854}, peerreviewed = {Yes}, title = {{Evolution} in quantum causal histories}, volume = {20}, year = {2003} } @misc{faucris.118832824, author = {Lohberger, Johannes and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Doubly} special relativity}, year = {2014} } @article{faucris.122248544, author = {Giesel, Kristina and Oelmann, Almut}, faupublication = {yes}, journal = {Acta Physica Polonica B}, pages = {339-349}, peerreviewed = {Yes}, title = {{Comparison} {Between} {Dirac} and {Reduced} {Quantization} in {LQG}-{Models} with {Klein}-{Gordon} {Scalar} {Fields}}, volume = {Acta Phys.Polon.Supp.}, year = {2017} } @article{faucris.115336364, abstract = {Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes' theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions.The abelian theory considered in the present article is the test case for our method. It can also be applied to the non-abelian theory. Results will be reported in a companion article. © 2011 Elsevier B.V.}, author = {Sahlmann, Hanno and Thiemann, Thomas}, doi = {10.1016/j.geomphys.2011.10.012}, faupublication = {yes}, journal = {Journal of Geometry and Physics}, keywords = {Abelian Chern-Simons theory; Generalized connections; Loop quantum gravity}, pages = {204-212}, peerreviewed = {Yes}, title = {{Abelian} {Chern}-{Simons} theory, {Stokes}' theorem, and generalized connections}, volume = {62}, year = {2012} } @article{faucris.120703484, abstract = {The Hamiltonian constraint is the key element of the canonical formulation of loop quantum gravity (LQG) coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so-called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations. © 2013 American Physical Society.}, author = {Liegener, Klaus and Alesci, Emanuele and Zipfel, Antonia}, doi = {10.1103/PhysRevD.88.084043}, faupublication = {yes}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {Yes}, title = {{Matrix} elements of {Lorentzian} {Hamiltonian} constraint in loop quantum gravity}, volume = {88}, year = {2013} } @article{faucris.123693064, abstract = {This paper is the first in a series of seven papers with the title 'quantum spin dynamics (QSD)'.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {839-873}, peerreviewed = {Yes}, title = {{Quantum} spin dynamics ({QSD})}, volume = {15}, year = {1998} } @article{faucris.119297684, abstract = {The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge invariant formalism is used to compute the evolution equations of linear perturbations around a general relativistic spacetime background in the Jordan frame. These equations are then specialized to the case of a flat FRW cosmological background. Furthermore, the equivalence between the Jordan frame and the Einstein frame of STT in the manifestly gauge invariant Hamiltonian formalism is analyzed, and it is shown that also in this framework they can be related by a conformal transformation. Finally, the obtained evolution equations for the linear perturbations in our formalism are compared with those in the standard cosmological perturbation theory. It turns out that the perturbation equations in the two different formalisms coincide with each other in a suitable limit.}, author = {Han, Yu and Giesel, Kristina and Ma, Yongge}, doi = {10.1088/0264-9381/32/13/135006}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, keywords = {scalar-tensor theories of gravity;cosmological perturbation theory;manifestly gauge invariant perturbations}, peerreviewed = {Yes}, title = {{Manifestly} gauge invariant perturbations of scalar-tensor theories of gravity}, volume = {32}, year = {2015} } @article{faucris.123560184, abstract = {The Duflo map is a valuable tool for operator ordering in contexts in which Kirillov-Kostant brackets and their quantizations play a role. A priori, the Duflo map is only defined on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. Here we discuss extensions to the whole symmetric algebra, as well as their application to the calculation of Chern-Simons theory expectation values.}, author = {Sahlmann, Hanno and Zilker, Thomas}, doi = {10.1016/j.geomphys.2017.07.022}, faupublication = {yes}, journal = {Journal of Geometry and Physics}, pages = {297 - 308}, peerreviewed = {Yes}, title = {{Extensions} of the {Duflo} map and {Chern}-{Simons} expectation values}, volume = {121}, year = {2017} } @phdthesis{faucris.111430484, author = {Bodendorfer, Norbert and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Loop} {Quantization} of {Supergravity} {Theories}}, year = {2013} } @article{faucris.109463024, abstract = {Utilizing the unique and reliable ultrasmall-x predictions of the dynamical (radiative) parton model, nominal event rates and their detailed energy dependence caused by a variety of cosmic UHE neutrino fluxes are calculated and analyzed. In addition, maximal Regge-model inspired small-x structure functions are employed for obtaining optimal rates which do not necessarily require 'new'physics interpretations. Upward mu(+) + mu(-) event rates are estimated by taking into account total and nadir-angle dependent regeneration effects due to neutral current interactions. For exploring extragalactic neutrino sources at highest energies (greater than or similar to 10(8) GeV) with modern (future) ground-level telescopes, we analyze horizontal air shower event rates and shower events caused by Earth-skimming tau-neutrinos, in particular their detailed shower- and cosmic neutrino-energy dependence. As an illustration of 'new physics' implications we estimate the relevant horizontal air shower event rates due to spin-2 Kaluza-Klein 'graviton' exchanges in neutral current neutrino-quark and neutrino-gluon interactions at low TeV-scales. (C) 2003 Elsevier B.V. All rights reserved.}, author = {Giesel, Kristina and Jureit, Jan-Hendrik and Reya, Ewald}, doi = {10.1016/S0927-6505(03)00191-9}, faupublication = {no}, journal = {Astroparticle Physics}, pages = {335-360}, peerreviewed = {Yes}, title = {{Cosmic} {UHE} neutrino signatures}, volume = {20}, year = {2003} } @article{faucris.110403744, abstract = {Spin-foam models are supposed to be discretized path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration is that no consensus has been reached for how to implement the simplicity constraints. Indeed, none of these models strictly follows from the original path integral with commuting B fields, rather, by some nonstandardmanipulations one always ends up with non-commuting B fields and the simplicity constraints become in fact anomalous which is the source for there being several inequivalent strategies to circumvent the associated problems. In this paper, we construct a new Euclidian spin-foam model which is constructed by standard methods from the Plebanski-Holst path integral with commuting B fields discretized on a 4D simplicial complex. The resulting model differs from the current ones in several aspects, one of them being that the closure constraint needs special care. Only when dropping the closure constraint by hand and only in the large spin limit can the vertex amplitudes of this model be related to those of the FK gamma. model but even then the face and edge amplitude differ. Interestingly, a non-commutative deformation of the B-IJ variables leads from our new model to the Barrett-Crane model in the case of gamma =infinity.}, author = {Han, Muxin and Thiemann, Thomas}, doi = {10.1088/0264-9381/30/23/235024}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Commuting} simplicity and closure constraints for {4D} spin-foam models}, volume = {30}, year = {2013} } @article{faucris.118263464, abstract = {Finally, we comment on the status of the Wick rotation transform in the light of the present results and give an intuitive description of the action of the Hamiltonian constraint.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {875-905}, peerreviewed = {Yes}, title = {{Quantum} spin dynamics ({QSD}): {II}. {The} kernel of the {Wheeler}-{DeWitt} constraint operator}, volume = {15}, year = {1998} } @article{faucris.214173102, abstract = {A spin-foam model is derived from the canonical model of loop quantum gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of loop quantum cosmology by Ashtekar et al (2009 Phys. Len. B 681 347-52), later developed by Henderson et al (2011 Glass. Quantum Grav. 28 025003).}, author = {Kisielowski, Marcin and Lewandowski, Jerzy}, doi = {10.1088/1361-6382/aafcc0}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, note = {CRIS-Team WoS Importer:2019-03-22}, peerreviewed = {Yes}, title = {{Spin}-foam model for gravity coupled to massless scalar field}, volume = {36}, year = {2019} } @misc{faucris.111477124, author = {Roelcke, Carmen and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Conical} space-time defects and their phenomenological consequences}, year = {2015} } @article{faucris.123835184, abstract = {Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e. g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge-invariant degrees of freedom which allow unambiguous comparison between theory and experiment. When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to nth order in terms of quantities that are gauge-invariant up to terms of higher orders becomes highly non-trivial and cumbersome. This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature. In this series of papers we circumvent these difficulties by passing to a manifestly gauge-invariant framework. In other words, we only perturb gauge-invariant, i.e. measurable quantities, rather than gauge variant ones. Thus, gauge invariance is preserved non-perturbatively while we construct the perturbation theory for the equations of motion for the gauge-invariant observables to all orders. In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchar as well as the relational formalism due to Rovelli. In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order. As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment. However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge-invariant generalization to higher orders. This will also allow us to settle the stability issue in a future publication.}, author = {Giesel, Kristina and Hofmann, Stefan and Thiemann, Thomas and Winkler, Oliver}, doi = {10.1088/0264-9381/27/5/055005}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Manifestly} gauge-invariant general relativistic perturbation theory: {I}. {Foundations}}, volume = {27}, year = {2010} } @masterthesis{faucris.111021944, abstract = {Gaussian path integrals play an important role for free quantum field theories, and for the perturbative treatment of interacting quantum field theories. These path integrals are defined via measures on linear spaces. For loop quantum gravity, a framework for path integrals over spaces of connections was developed. Some examples of what one could call Gaussian measures are known. They are interesting, among other things, because they give the connections finite quantum mechanical fluctuations.

},
author = {Nekovar, Stefan and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Gaussian} {Measures} and {Representations} of the {Holonomy}-{Flux} {Algebra}},
year = {2014}
}
@inproceedings{faucris.110424644,
author = {Kastrup, Hans and Thiemann, Thomas},
faupublication = {no},
month = {Jan},
pages = {158-172},
peerreviewed = {unknown},
title = {{Spherically} symmetric gravity and the notion of time in {General} {Relativity}},
year = {1995}
}
@masterthesis{faucris.121937244,
author = {Reichert, Thorsten and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Quantum} {Mechanics} in the {Polymer} {Particle} {Representation}},
year = {2013}
}
@article{faucris.123229084,
abstract = {We investigate several conceptual and technical details that might be of interest for full (3 + 1) gravity. We use the new canonical variables introduced by Ashtekar, which simplifies the analysis tremendously.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Nuclear Physics B},
pages = {681-720},
peerreviewed = {Yes},
title = {{THE} {REDUCED} {PHASE}-{SPACE} {OF} {SPHERICALLY} {SYMMETRICAL} {EINSTEIN}-{MAXWELL} {THEORY} {INCLUDING} {A} {COSMOLOGICAL} {CONSTANT}},
volume = {436},
year = {1995}
}
@article{faucris.118959984,
abstract = {Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic observables of the theory, the Ashtekar-Isham-Lewandowski (AIL) representation, has been constructed. Recently, several uniqueness results for this representation have been worked out. In the present paper, we contribute to these efforts by showing that the AIL representation is irreducible, provided it is viewed as the representation of a certain C*-algebra which is very similar to the Weyl algebra used in the canonical quantization of free quantum field theories. © 2006 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/13/010},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {4453-4471},
peerreviewed = {Yes},
title = {{Irreducibility} of the {Ashtekar}-{Isham}-{Lewandowski} representation},
volume = {23},
year = {2006}
}
@article{faucris.109996304,
abstract = {The Hartle-Hawking state is a proposal for a preferred initial state for quantum gravity, based on a path integral over all compact Euclidean four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the (Lorentzian) Hamiltonian constraint of general relativity in ADM variables in a formal sense. In this article, we address the question of whether this construction is dependent on the canonical variables used. We give a precise derivation of the properties of the Hartle-Hawking state in terms of formal manipulations of the path integral expressions. Then we mimic the construction in terms of Ashtekar-Barbero variables, and observe that the resulting wave function does not satisfy the Lorentzian Hamiltonian constraint even in a formal sense. We also investigate this issue for the relativistic particle, with a similar conclusion. We finally suggest a modification of the proposal that does satisfy the constraint at least in a formal sense and start to consider its implications in quantum cosmology. We find that for certain variables, and in the saddle point approximation, the state is very similar to the Ashtekar-Lewandowski state of loop quantum gravity. In the process, we have calculated the on-shell action for several cosmological models in connection variables.},
author = {Dhandhukiya, Satya and Sahlmann, Hanno},
doi = {10.1103/PhysRevD.95.084047},
faupublication = {yes},
journal = {Physical Review D},
peerreviewed = {unknown},
title = {{Towards} {Hartle}-{Hawking} states for connection variables},
volume = {95},
year = {2017}
}
@masterthesis{faucris.109628024,
author = {Herzog, Adrian and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Geometrical} {Clocks} in {Cosmological} {Perturbation} {Theory}},
year = {2017}
}
@article{faucris.201148142,
abstract = {We describe the quantum theory of isolated horizons with electromagnetic or non-Abelian gauge charges in a setting in which both the gauge and gravitational field are quantized. We consider the distorted case, and its spherically symmetric limit. We show that the gravitational horizon d.o.f. give rise to the Bekenstein-Hawking relation, with lower-order terms giving some corrections for small black holes. We also demonstrate that one can include matter d.o.f. in the state counting. We show that one can expect (potentially divergent) contributions proportional to the area, as well as logarithmic corrections proportional to the horizon charge. This is qualitatively similar to results on matter contributions obtained with other methods in the literature.},
author = {Sahlmann, Hanno and Eder, Konstantin},
doi = {10.1103/PhysRevD.97.086016},
faupublication = {yes},
journal = {Physical Review D},
peerreviewed = {Yes},
title = {{Quantum} theory of charged isolated horizons},
volume = {97},
year = {2018}
}
@misc{faucris.114587484,
abstract = {

},
author = {Lang, Thorsten and et al.},
author_hint = {Lang T, Thiemann T},
faupublication = {yes},
peerreviewed = {automatic},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Hawking} {Radiation}},
year = {2011}
}
@phdthesis{faucris.121572704,
author = {Stottmeister, Alexander and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{On} the {Embedding} of {Quantum} {Field} {Theory} on {Curved} {Spacetimes} into {Loop} {Quantum} {Gravity}},
year = {2015}
}
@article{faucris.115370684,
abstract = {Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of (kinematical) observables and of a representation of A on a measure space over the space of generalized connections. This representation is singled out by its elegance and diffeomorphism covariance. Recently, in the context of the quest for semiclassical states, states of the theory in which the quantum gravitational field is close to some classical geometry, it was realized that it might also be worthwhile to study different representations of the algebra A. The content of the present work is the observation that under some mild assumptions, the mathematical structure of representations of A can be analyzed rather effortlessly, to a certain extent: each representation can be labeled by sets of functions and measures on the space of (generalized) connections that fulfill certain conditions. © 2011 American Institute of Physics.},
author = {Sahlmann, Hanno},
doi = {10.1063/1.3525705},
faupublication = {no},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Some} results concerning the representation theory of the algebra underlying loop quantum gravity},
volume = {52},
year = {2011}
}
@article{faucris.123223584,
abstract = {In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a Chern-Simons theory on the boundary in the four-dimensional case, to non-distorted isolated horizons in 2(n + 1)-dimensional spacetimes. The key idea is to generalize the four-dimensional isolated horizon boundary condition by using the Euler topological density E-(2n) of a spatial slice of the black hole horizon as a measure of distortion. The resulting symplectic structure on the horizon coincides with the one of higher-dimensional SO(2(n + 1))-Chern-Simons theory in terms of a Peldan-type hybrid connection Gamma(0) and resembles closely the usual treatment in (3 + 1) dimensions. We comment briefly on a possible quantization of the horizon theory. Here, some subtleties arise since higher-dimensional non-Abelian Chern-Simons theory has local degrees of freedom. However, when replacing the natural generalization to higher dimensions of the usual boundary condition by an equally natural stronger one, it is conceivable that the problems originating from the local degrees of freedom are avoided, thus possibly resulting in a finite entropy.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/31/5/055002},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {loop quantum gravity;higher dimensions;black holes;Chern-Simons theory},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {V}. {Isolated} horizon boundary degrees of freedom},
volume = {31},
year = {2014}
}
@article{faucris.121880924,
abstract = {In effective models of loop quantum cosmology, the holonomy corrections are associated with deformations of space-time symmetries. The most evident manifestation of the deformations is the emergence of a Euclidean phase accompanying the nonsingular bouncing dynamics of the scale factor. In this article, we compute the power spectrum of scalar perturbations generated in this model, with a massive scalar field as the matter content. Instantaneous and adiabatic vacuum-type initial conditions for scalar perturbations are imposed in the contracting phase. The evolution through the Euclidean region is calculated based on the extrapolation of the time direction pointed by the vectors normal to the Cauchy hypersurface in the Lorentzian domains. The obtained power spectrum is characterized by a suppression in the IR regime and oscillations in the intermediate energy range. Furthermore, the speculative extension of the analysis in the UV reveals a specific rise of the power leading to results incompatible with the data.},
author = {Schander, Susanne and Barrau, Aurelien and Bolliet, Boris and Linsefors, Linda and Mielczarek, Jakub and Grain, Julien},
doi = {10.1103/PhysRevD.93.023531},
faupublication = {no},
journal = {Physical Review D},
month = {Jan},
peerreviewed = {Yes},
title = {{Primordial} scalar power spectrum from the {Euclidean} big bounce},
volume = {93},
year = {2016}
}
@article{faucris.110372284,
abstract = {In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Published by AIP},
author = {Stottmeister, Alexander and Thiemann, Thomas},
doi = {10.1063/1.4960823},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Coherent} states, quantum gravity, and the {Born}-{Oppenheimer} approximation. {III}.: {Applications} to loop quantum gravity},
volume = {57},
year = {2016}
}
@article{faucris.123620244,
abstract = {We derive a canonical algorithm to obtain this holomorphic representation and in particular explicitly compute it for quantum gravity in terms of a Wick rotation transform.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1383-1403},
peerreviewed = {Yes},
title = {{Reality} conditions inducing transforms for quantum gauge field theory and quantum gravity},
volume = {13},
year = {1996}
}
@misc{faucris.119643304,
author = {Zöbelein, Carolin and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Dirac}-{Observablen} in der {Kosmolgie}},
year = {2013}
}
@article{faucris.120859904,
abstract = {The volume operator plays a pivotal role for the quantum dynamics of loop quantum gravity (LQG). It is essential to construct triad operators that enter the Hamiltonian constraint and which become densely defined operators on the full Hilbert space, even though in the classical theory the triad becomes singular when classical GR breaks down. The expression for the volume and triad operators derives from the quantization of the fundamental electric flux operator of LQG by a complicated regularization procedure. In fact, there are two inequivalent volume operators available in the literature and, moreover, both operators are unique only up to a finite, multiplicative constant which should be viewed as a regularization ambiguity. Now on the one hand, classical volumes and triads can be expressed directly in terms of fluxes and this fact was used to construct the corresponding volume and triad operators. On the other hand, fluxes can be expressed in terms of triads and triads can be replaced by Poisson brackets between the holonomy and the volume operators. Therefore one can also view the holonomy operators and the volume operator as fundamental and consider the flux operator as a derived operator. In this paper we mathematically implement this second point of view and thus can examine whether the volume, triad and flux quantizations are consistent with each other. The results of this consistency analysis are rather surprising. Among other findings we show the following. ( 1) The regularization constant can be uniquely fixed. ( 2) One of the volume operators can be ruled out as inconsistent. ( 3) Factor ordering ambiguities in the definition of triad operators are immaterial for the classical limit of the derived flux operator. The results of this paper show that within full LQG triad operators are consistently quantized.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/18/011},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {5667-5691},
peerreviewed = {Yes},
title = {{Consistency} check on volume and triad operator quantization in loop quantum gravity: {I}},
volume = {23},
year = {2006}
}
@misc{faucris.123776664,
author = {Stritzelberger, Nadine and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Geometrische} {Eigenschaften} der {Verschränkungsentropie} in der {Loop}-{Quantengravitation}},
year = {2014}
}
@article{faucris.201147872,
abstract = {We study the asymptotic behaviour of the vertex amplitude for the EPRL spin foam model extended to include timelike tetrahedra. We analyze both, tetrahedra of signature --- (standard EPRL), as well as of signature +-- (Hnybida-Conrady extension), in a unified fashion. However, we assume all faces to be of signature --. We find that the critical points of the extended model are described again by 4-simplices and the phase of the amplitude is equal to the Regge action. Interestingly, in addition to the Lorentzian and Euclidean sectors there appear also split signature 4-simplices.},
author = {Sahlmann, Hanno and Kaminski, Wojciech and Kisielowski, Marcin},
doi = {10.1088/1361-6382/aac6a4},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {quantum gravity;spin foam;EPRL model;stationary phase analysis;large spin limit},
peerreviewed = {Yes},
title = {{Asymptotic} analysis of the {EPRL} model with timelike tetrahedra},
volume = {35},
year = {2018}
}
@article{faucris.123226004,
abstract = {The framework developed here is the classical cornerstone on which the semiclassical analysis in a new series of papers called `gauge theory coherent states' is based.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {3293-3338},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD}): {VII}. {Symplectic} structures and continuum lattice formulations of gauge field theories},
volume = {18},
year = {2001}
}
@article{faucris.123505404,
abstract = {In this paper, we study the no-boundary wavefunction in scalartensor gravity with various potentials for the non-minimally coupled scalar field. Our goal is to calculate probabilities for the scalar fieldand hence the effective gravitational coupling and cosmological constantto take specific values. Most calculations are performed in the minisuperspace approximation, and we use a saddle point approximation for the Euclidean action, which is then evaluated numerically. We find that for potentials that have several minima, none of them is substantially preferred by the quantum-mechanical probabilities. We argue that the same is true for the stable and the runaway solution in the case of a dilaton-type potential. Technically, this is due to the inclusion of quantum-mechanical effects (fuzzy instantons). These results are in contrast to the often-held view that vanishing gravitation or cosmological constants would be exponentially preferred in quantum cosmology, and they may be relevant to the cosmological constant problem and the dilaton stabilization problem. © 2012 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Yeom, Dong-han and Hwang, Dong-il},
doi = {10.1088/0264-9381/29/9/095005},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{The} no-boundary measure in scalar-tensor gravity},
volume = {29},
year = {2012}
}
@article{faucris.215878945,
abstract = {We use the freedom available in hybrid loop quantum cosmology to split the degrees of freedom between the geometry and the matter fields so as to build a quantum field theory for the matter content with good quantum properties. We investigate this issue in an inflationary, flat cosmology with inhomogeneous perturbations, and focus the discussion on a Dirac field, minimally coupled to the cosmological background and treated as a perturbation. After truncating the action at the lowest nontrivial order in perturbations, one must define canonical variables for the matter content, for which one generally employs canonical transformations that mix the homogeneous background and the perturbations. Each of these possible definitions comes associated with a different matter contribution to the Hamiltonian of the complete system, that may, in general, contain terms that are quadratic in creation like variables, and in annihilation like variables, with the subsequent production and destruction of pairs of fermionic particles and antiparticles. We determine a choice of the fermionic canonical variables for which the interaction part of the Hamiltonian can be made as negligible as desired in the asymptotic regime of large particle/ antiparticle wave numbers. Finally, we study the quantum dynamics for this choice, imposing the total Hamiltonian constraint on the quantum states and assuming that their gravitational part is not affected significantly by the presence of fermions. In this way, we obtain a Schrodinger equation for the fermionic degrees of freedom in terms of quantum expectation values of the geometry that leads to asymptotically diagonal Heisenberg relations and Bogoliubov evolution transformations, with no divergences in the associated normal-ordered Hamiltonian.},
author = {Elizaga de Navascués, Beatriz and Mena Marugan, Guillermo A. and Prado, Santiago},
doi = {10.1103/PhysRevD.99.063535},
faupublication = {yes},
journal = {Physical Review D},
note = {CRIS-Team WoS Importer:2019-04-12},
peerreviewed = {Yes},
title = {{Asymptotic} diagonalization of the fermionic {Hamiltonian} in hybrid loop quantum cosmology},
volume = {99},
year = {2019}
}
@article{faucris.110423104,
abstract = {The quantum symmetry algebra corresponding to the generators of the little group faithfully represents the classical algebra.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1463-1485},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD}): {VI}. {Quantum} {Poincare} algebra and a quantum positivity of energy theorem for canonical quantum gravity},
volume = {15},
year = {1998}
}
@article{faucris.123221604,
abstract = {Recently, substantial amount of activity in quantum general relativity (QGR) has focused on the semiclassical analysis of the theory. In this paper, we want to comment on two such developments: (1) polymer-like states for Maxwell theory and linearized gravity constructed by Varadarajan which use much of the Hilbert space machinery that has proved useful in QGR, and (2) coherent states for QGR, based on the general complexifier method, with built-in semiclassical properties. We show the following. (A) Varadarajan's states are complexifier coherent states. This unifies all states constructed so far under the general complexifier principle. (B) Ashtekar and Lewandowski suggested a non-Abelian generalization of Varadarajan's states to QGR which, however, are no longer of the complexifier type. We construct a new class of non-Abelian complexifiers which come close to that underlying Varadarajan's construction. (C) Non-Abelian complexifiers close to Varadarajan's induce new types of Hilbert spaces which do not support the operator algebra of QGR. The analysis suggests that if one sticks to the present kinematical framework of QGR and if kinematical coherent states are at all useful, then normalizable, graph-dependent states must be used which are produced by the complexifier method as well. (D) Present proposals for states with mildened graph dependence, obtained by performing a graph average, do not approximate well coordinate-dependent observables. However, graph-dependent states, whether averaged or not, seem to be well suited for the semiclassical analysis of QGR with respect to coordinate-independent operators.},
author = {Thiemann, Thomas},
doi = {10.1088/0264-9381/23/6/013},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2063-2117},
peerreviewed = {Yes},
title = {{Complexifier} coherent states for quantum general relativity},
volume = {23},
year = {2006}
}
@phdthesis{faucris.121044704,
author = {Thurn, Andreas and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Higher} {Dimensional} and {Supersymmetric} {Extensions} of {Loop} {Quantum} {Gravity}},
year = {2013}
}
@article{faucris.110402644,
abstract = {An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic 'Lebesgue measure' usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed. In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element. From this path integral for the Holst formulation of general relativity we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical loop quantum gravity and the spin-foam approach.},
author = {Engle, Jonathan and Han, Muxin and Thiemann, Thomas},
doi = {10.1088/0264-9381/27/24/245014},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Canonical} path integral measures for {Holst} and {Plebanski} gravity: {I}. {Reduced} phase space derivation},
volume = {27},
year = {2010}
}