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.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.109458404, abstract = {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} } @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} } @inproceedings{faucris.123226444, abstract = {We use the new canonical variables introduced by Ashtekar which simplifies the analysis tremendously.}, author = {Thiemann, Thomas}, faupublication = {no}, pages = {293-298}, peerreviewed = {unknown}, publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD}, title = {{REDUCED} {PHASE}-{SPACE} {QUANTIZATION} {OF} {SPHERICALLY} {SYMMETRICAL} {EINSTEIN}-{MAXWELL} {THEORY} {INCLUDING} {A} {COSMOLOGICAL} {CONSTANT}}, volume = {3}, year = {1994} } @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} } @masterthesis{faucris.111491864, author = {Böhm, Benedikt and Giesel, Kristina}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{The} {Physical} {Hamiltonian} of the {Gowdy} {Model} in {Algebraic} {Quantum} {Gravity}}, year = {2015} } @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.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} } @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} } @misc{faucris.111490764, author = {Reichert, Thorsten and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Angular} {Momentum} and {Quantum} {Gravity}}, year = {2010} } @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.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.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.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} } @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} } @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} } @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.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} } @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.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.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} } @article{faucris.110411884, abstract = {There is a gap that has not been filled since the formulation of general relativity in terms of Ashtekar's new variables, namely the treatment of asymptotically flat field configurations that are general enough to be able to define the generators of the Lorentz subgroup of the asymptotic Poincare group. While such a formulation already exists for the old geometrodynamical variables, up to now only the generators of the translation subgroup have been able to be defined, because the function spaces of the fields considered earlier are taken in too special a form. The transcription of the framework from the ADM variables to Ashtekar's variables turns out not to be straightforward, due to the a priori freedom to choose the internal SO(3) frame at spatial infinity, and due to the fact that the non-trivial reality conditions of the Ashtekar framework re-enter the stage when imposing suitable boundary conditions on the fields and the Lagrange multipliers.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, month = {Jan}, pages = {181-198}, peerreviewed = {Yes}, title = {{GENERALIZED} {BOUNDARY}-{CONDITIONS} {FOR} {GENERAL}-{RELATIVITY} {FOR} {THE} {ASYMPTOTICALLY} {FIAT} {CASE} {IN} {TERMS} {OF} {ASHTEKARS} {VARIABLES}}, volume = {12}, year = {1995} } @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.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.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} } @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} } @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.

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} } @incollection{faucris.116261244, abstract = {We introduce a notion of a weak Poisson structure on a manifold

-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.123219624,
abstract = {We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four space-time dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state-independent factor. (C) 1998 American Institute of Physics.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Journal of Mathematical Physics},
pages = {3347-3371},
peerreviewed = {Yes},
title = {{Closed} formula for the matrix elements of the volume operator in canonical quantum gravity},
volume = {39},
year = {1998}
}
@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}
}
@article{faucris.110416284,
abstract = {In this paper, we discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional general relativity and supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D >= 3 in Class. Quantum Grav. 30 045003, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one can choose a subset of quadratic simplicity constraint operators which are non-anomalous among themselves and allow for a natural unitary map of the spin networks in the kernel of these simplicity constraint operators to the SU(2)-based Ashtekar-Lewandowski Hilbert space in D = 3. The linear constraint operators on the other hand are non-anomalous by themselves; however, their solution space is shown to differ in D = 3 from the expected Ashtekar-Lewandowski Hilbert space. We comment on possible strategies to make a connection to the quadratic theory. Also, we comment on the relation of our proposals to the existing work in the spin foam literature and how these works could be used in the canonical theory. We emphasize that many ideas developed in this paper are certainly incomplete and should be considered as suggestions for possible starting points for more satisfactory treatments in the future.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045005},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{On} the implementation of the canonical quantum simplicity constraint},
volume = {30},
year = {2013}
}
@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}
}
@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.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}
}
@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.

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.109131704,
abstract = {We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of (a) the Brown-Kuchar mechanism in the presence of pressure-free dust fields which allows to deparametrize the theory and (b) Rovelli's relational formalism in the extended version developed by Dittrich to construct the algebra of gauge-invariant observables. Since the resulting algebra of observables is very simple, one can quantize it using the methods of LQG. Basically, the kinematical Hilbert space of non-reduced LQG now becomes a physical Hilbert space and the kinematical results of LQG such as discreteness of spectra of geometrical operators now have physical meaning. The constraints have disappeared; however, the dynamics of the observables is driven by a physical Hamiltonian which is related to the Hamiltonian of the standard model (without dust) and which we quantize in this paper.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/27/17/175009},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Algebraic} quantum gravity ({AQG}): {IV}. {Reduced} phase space quantization of loop quantum gravity},
volume = {27},
year = {2010}
}
@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}
}
@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}
}
@misc{faucris.124241084,
author = {Bärenz, Manuel and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Cartan} {Geometries} and {Spin} {Network} {Quantisation}},
year = {2011}
}
@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} } @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.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} } @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.118419444, abstract = {QGR therefore is, by definition, not a unified theory of all interactions in the standard sense, since such a theory would require a new symmetry principle. However, it unifies all presently known interactions in a new sense by quantum mechanically implementing their common symmetry group, the four-dimensional diffeomorphism group, which is almost completely broken in perturbative approaches.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Lecture Notes in Physics}, month = {Jan}, pages = {41-135}, peerreviewed = {unknown}, title = {{Lectures} on {Loop} {Quantum} {Gravity}}, volume = {631}, year = {2003} } @article{faucris.115373104, abstract = {In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this steplike behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking. © 2007 The American Physical Society.}, author = {Sahlmann, Hanno}, doi = {10.1103/PhysRevD.76.104050}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {Yes}, title = {{Toward} explaining black hole entropy quantization in loop quantum gravity}, volume = {76}, year = {2007} } @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.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} } @article{faucris.108346964, abstract = {We quantize the new connection formulation of (D + 1)-dimensional general relativity developed in our companion papers by loop quantum gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalize to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its 'diagonal' components acting at edges of spin-network functions are easily solved, its 'off-diagonal' components acting at vertices are non-trivial and require a more elaborate treatment.}, author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas}, doi = {10.1088/0264-9381/30/4/045003}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{New} variables for classical and quantum gravity in all dimensions: {III}. {Quantum} theory}, volume = {30}, year = {2013} } @article{faucris.110426404, abstract = {The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections module gauge transformations. Since this space is a compact Hausdorff space, conversely, we know from the Riesz-Markov theorem that every positive linear functional on the space of continuous functions thereon qualifies as the loop transform of a regular Borel measure on the moduli space. In the present article we show how one can compute the finite joint distributions of a given characteristic functional, that is, we derive the inverse loop transform. (C) 1998 American Institute of Physics. [S002-2488(98)00302-8].}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Journal of Mathematical Physics}, pages = {1236-1248}, peerreviewed = {Yes}, title = {{The} inverse loop transform}, volume = {39}, year = {1998} } @article{faucris.123917244, abstract = {We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which an SU(2) connection is diagonal and it is therefore surprising that the operator obtained after regularization is densely defined, does not suffer from factor ordering singularities, and does not require any renormalization. We show that the length operator admits self-adjoint extensions and compute part of its spectrum which, like its companions, the volume and area operators already constructed in the literature, is purely discrete and roughly quantized in units of the Planck length. The length operator contains full and direct information about all the components of the metric tensor which facilitates the construction of so-called weave states which approximate a given classical three-geometry. (C) 1998 American Institute of Physics.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Journal of Mathematical Physics}, pages = {3372-3392}, peerreviewed = {Yes}, title = {{A} length operator for canonical quantum gravity}, volume = {39}, year = {1998} } @article{faucris.108872324, abstract = {We investigate the no-boundary measure in the context of moduli stabilization. To this end, we first show that for exponential potentials, there are no classical histories once the slope exceeds a critical value. We also investigate the probability distributions given by the no-boundary wavefunction near maxima of the potential. These results are then applied to a simple model that compactifies 6D to 4D (HBSV model) with fluxes. We find that the no-boundary wavefunction effectively stabilizes the moduli of the model. Moreover, we find the a priori probability for the cosmological constant in this model. We find that a negative value is preferred, and a vanishing cosmological constant is not distinguished by the probability measure. We also discuss the application to the cosmic landscape. Our preliminary arguments indicate that the probability of obtaining anti-de Sitter space is vastly greater than that for de Sitter. © 2012 IOP Publishing Ltd.}, author = {Hwang, Dong-il and Lee, Bum-Hoon and Sahlmann, Hanno and Yeom, Dong-han}, doi = {10.1088/0264-9381/29/17/175001}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{The} no-boundary measure in string theory: {Applications} to moduli stabilization, flux compactification and cosmic landscape}, volume = {29}, year = {2012} } @inproceedings{faucris.108293944, author = {Thiemann, Thomas}, faupublication = {no}, month = {Jan}, pages = {585-587}, peerreviewed = {unknown}, title = {{CANONICAL} {QUANTIZATION} {OF} {A} {MINISUPERSPACE} {MODEL} {FOR} {GRAVITY} {USING} {SELF}-{DUAL} {VARIABLES}}, year = {1994} } @article{faucris.108971984, abstract = {Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations which are predictive, interpretable, and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry: the latter must be hyperbolic, time-orientable, and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics-for the general tensorial spacetime geometries satisfying the above minimum requirements-is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus, the search for modified gravitational dynamics is reduced to a clear mathematical task.}, author = {Giesel, Kristina and Schuller, Frederic and Witte, Christof and Wolfarth, Matthias}, doi = {10.1103/PhysRevD.85.104042}, faupublication = {yes}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {Yes}, title = {{Gravitational} dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter}, volume = {85}, year = {2012} } @article{faucris.110403084, abstract = {The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group G with its normalized Haar measure mu(H), the Hall transform is an isometric isomorphism hem L(2)(G, mu(H)) to H(G(C)) boolean AND L(2)(G(C), v), where G(C) the complexification of G, H(G(C)) the space of holomorphic functions on G(C), and v an appropriate heat-kernel measure on G(C). We extend the Hall transform to the infinite dimensional context of non-Abelian gauge theories by replacing the Lie group G by (a certain extension of) the space A/g of connections module gauge transformations. The resulting ''coherent state transform'' provides a holomorphic representation of the holonomy C* algebra of real gauge fields. This representation is expected to play a key role in a non-perturbative, canonical approach to quantum gravity in 4 dimensions. (C) 1996 Academic Press, Inc.}, author = {Ashtekar, Abhay and Lewandowski, Jerzy and Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas}, faupublication = {no}, journal = {Journal of Functional Analysis}, pages = {519-551}, peerreviewed = {Yes}, title = {{Coherent} state transforms for spaces of connections}, volume = {135}, year = {1996} } @article{faucris.107121564, abstract = {In this paper, we carry out the counting of states for a black hole in loop quantum gravity, assuming however an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a nice and simplifying 'laboratory' for questions about the full theory. © 2008 IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/0264-9381/25/5/055004}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Entropy} calculation for a toy black hole}, volume = {25}, year = {2008} } @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.123229524, abstract = {Should nature be supersymmetric, then it will be described by Quantum Supergravity at least in some energy regimes. The currently most advanced description of Quantum Supergravity and beyond is Superstring Theory/M-Theory in 10/11 dimensions. String Theory is a top-to-bottom approach to Quantum Supergravity in that it postulates a new object, the string, from which classical Supergravity emerges as a low energy limit. On the other hand, one may try more traditional bottom-to-top routes and apply the techniques of Quantum Field Theory. Loop Quantum Gravity (LQG) is a manifestly background independent and non-perturbative approach to the quantisation of classical General Relativity, however, so far mostly without supersymmetry. The main obstacle to the extension of the techniques of LQG to the quantisation of higher dimensional Supergravity is that LQG rests on a specific connection formulation of General Relativity which exists only in D + 1 = 4 dimensions. In this Letter we introduce a new connection formulation of General Relativity which exists in all space-time dimensions. We show that all LQG techniques developed in D + 1 = 4 can be transferred to the new variables in all dimensions and describe how they can be generalised to the new types of fields that appear in Supergravity theories as compared to standard matter, specifically Rarita-Schwinger and p-form gauge fields. (C) 2012 Elsevier B.V. All rights reserved.}, author = {Bodendorfer, Norbert and Thurn, Andreas and Thiemann, Thomas}, doi = {10.1016/j.physletb.2012.04.003}, faupublication = {yes}, journal = {Physics Letters B}, keywords = {Loop quantum gravity;Supergravity;Higher dimensional gravity}, pages = {205-211}, peerreviewed = {Yes}, title = {{Towards} {Loop} {Quantum} {Supergravity} ({LQSG})}, volume = {711}, year = {2012} } @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.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.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.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.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.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.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.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} } @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} } @article{faucris.122513644, abstract = {In the canonical approach to Lorentzian quantum general relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of a Hilbert space structure, which was later proved to be a faithful representation of the canonical commutation and adjointness relations of the quantum field algebra of diffeomorphism invariant gauge field theories by Ashtekar, Lewandowski, Marolf, Mourao and Thiemann. This Hilbert space, together with its generalization due to Baez and Sawin, is appropriate for semi-classical quantum general relativity if the spacetime is spatially compact. In the spatially non-compact case, however, an extension of the Hilbert space is needed in order to approximate metrics that are macroscopically nowhere degenerate. For this purpose, in this paper we apply the theory of the infinite tensor product (ITP) of Hilbert Spaces, developed by von Neumann more than sixty years ago, to quantum general relativity. The cardinality of the number of tensor product factors can take the value of any possible Cantor aleph, making this mathematical theory well suited to our problem in which a Hilbert space is attached to each edge of an arbitrarily complicated, generally infinite graph. The new framework opens access to a new arsenal of techniques, appropriate to describe fascinating physics such as quantum topology change, semi-classical quantum gravity, effective low-energy physics etc from the universal point of view of the ITP. In particular, the study of photons and gravitons propagating on fluctuating quantum spacetimes should now be in reach.}, author = {Thiemann, Thomas and Winkler, Oliver}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {4997-5053}, peerreviewed = {Yes}, title = {{Gauge} field theory coherent states ({GCS}): {IV}. {Infinite} tensor product and thermodynamical limit}, volume = {18}, year = {2001} } @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.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.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.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.120514944, abstract = {A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A comparison with more involved semiclassical techniques shows that there is agreement even at a quantitative level. Furthermore, by contrasting Hamiltonian and Lagrangian descriptions we show that possible Lorentz symmetry violations may be blurred as an artifact of the approximation scheme. Whether this is the case in a purely Hamiltonian analysis can be resolved by an improvement in the effective semiclassical analysis. © 2005 The American Physical Society.}, author = {Sahlmann, Hanno and Bojowald, Martin and Morales-Tecotl, Hugo}, doi = {10.1103/PhysRevD.71.084012}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, pages = {1-7}, peerreviewed = {unknown}, title = {{Loop} quantum gravity phenomenology and the issue of {Lorentz} invariance}, volume = {71}, year = {2005} } @article{faucris.110391424, abstract = {The Hamiltonian constraint remains the major unsolved problem in loop quantum gravity (LQG). Some time ago, a mathematically consistent candidate Hamiltonian constraint was proposed but there are still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper, we propose a solution to this set of problems based on the so-called master constraint which combines the smeared Hamiltonian constraints for all smearing functions into a single constraint. Due to a harmonic interplay of several mathematical facts, the problems with the commutator algebra disappear and chances are good that one can control the solution space and the (quantum) Dirac observables of LQG. Even a decision on whether the theory has the correct classical limit and a connection with the path integral (or spin foam) formulation could be in reach.}, author = {Thiemann, Thomas}, doi = {10.1088/0264-9381/23/7/002}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2211-2247}, peerreviewed = {Yes}, title = {{The} {Phoenix} {Project}: master constraint programme for loop quantum gravity}, volume = {23}, year = {2006} } @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.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.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.

}, 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} } @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} } @masterthesis{faucris.121097064, abstract = {String theory is one of the candidates for a theory that not only describes the nature of gravity at microscopic scales but also unites all fundamental forces into one common framework. This is possible by the simple assumption that all matter is given by small one-dimensional objects – strings – that may be open or closed.

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}
}
@misc{faucris.109907204,
author = {Giesel, Kristina and Herzog, Adrian},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Lie}-{Punktsymmetrien} erhaltende {Quantisierung} in der {Loop}-{Quantenkosmologie}},
year = {2014}
}
@article{faucris.201077232,
abstract = {Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism. We show that various gauge invariant variables obtained in the conventional analysis of cosmological perturbation theory correspond to Dirac observables tied to a specific choice of geometrical clocks. As examples, we show that the Bardeen potentials and the Mukhanov-Sasaki variable emerge naturally in our analysis as observables when gauge fixing conditions are determined via clocks in the Hamiltonian framework. Similarly other gauge invariant variables for various gauges can be systematically obtained. We demonstrate this by analyzing five common gauge choices: longitudinal, spatially flat, uniform field, synchronous and comoving gauge. For all these, we apply the observable map in the context of the relational formalism and obtain the corresponding Dirac observables associated with these choices of clocks. At the linear order, our analysis generalizes the existing results in canonical cosmological perturbation theory twofold. On the one hand we can include also gauges that can only be analyzed in the context of the extended ADM-phase space and furthermore, we obtain a set of natural gauge invariant variables, namely the Dirac observables, for each considered choice of gauge conditions. Our analysis provides insights on which clocks should be used to extract the relevant natural physical observables both at the classical and quantum level. We also discuss how to generalize our analysis in a straightforward way to higher orders in the perturbation theory to understand gauge conditions and the construction of gauge invariant quantities beyond linear order.

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.

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} } @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.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.115365844, abstract = {We follow arguments of Verlinde (2010 arXiv:1001.0785 [hep-th]) and Klinkhamer (2010 arXiv:1006.2094 [hep-th]), and construct two models of the microscopic theory of a holographic screen that allow for the thermodynamical derivation of Newton's law, with Newton's constant expressed in terms of a minimal length scale l contained in the area spectrum of the microscopic theory. One of the models is loosely related to the quantum structure of surfaces and isolated horizons in loop quantum gravity. Our investigation shows that the conclusions reached by Klinkhamer regarding the new length scale l seem to be generic in all their qualitative aspects. © 2011 IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/0264-9381/28/1/015006}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Newton}'s constant from a minimal length: {Additional} models}, volume = {28}, year = {2011} } @misc{faucris.109674664, author = {Wasserka, Tony and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Four}-valent vertex and the {Penrose} metric}, year = {2014} } @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.108973304, abstract = {..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consists of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level.}, author = {Giesel, Kristina and Domagala, Marcin and Kaminski, Wojciech and Lewandowski, Jerzy}, doi = {10.1103/PhysRevD.82.104038}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {Yes}, title = {{Gravity} quantized: {Loop} quantum gravity with a scalar field}, volume = {82}, year = {2010} } @phdthesis{faucris.123917024, author = {Lanéry, Suzanne and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Projective} {State} {Spaces} for {Theories} of {Connections}}, year = {2015} } @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.110388344, abstract = {In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than structure constants. Here We use this framework and propose how to implement explicitly a reduced phase space quantization of a given system, at least in principle, without the need to Compute the gauge equivalence classes. The degree of practicality of this programme depends on the choice of the partial observables involved. The (multi-fingered) time evolution was shown to correspond to an automorphism on the set of Dirac observables, so generated and interesting representations of the latter will be those for which a suitable preferred Subgroup is realized unitarily. We sketch how Such a programme might look for general relativity. We also observe that the ideas by Dittrich can be used in order to generate constraints equivalent to those of the Hamiltonian constraints for general relativity such that they are spatially diffeomorphism invariant. This has the important Consequence that one can now quantize the new Hamiltonian constraints on the partially reduced Hilbert space of spatially diffeomorphism invariant states, just as for the recently proposed master constraint programme.}, author = {Thiemann, Thomas}, doi = {10.1088/0264-9381/23/4/006}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {1163-1180}, peerreviewed = {Yes}, title = {{Reduced} phase space quantization and {Dirac} observables}, volume = {23}, year = {2006} } @article{faucris.118959324, abstract = {We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and an su(2)-valued one-form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similarly to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.}, author = {Sahlmann, Hanno and Pranzetti, Daniele}, doi = {10.1016/j.physletb.2015.04.070}, faupublication = {yes}, journal = {Physics Letters B}, pages = {209-216}, peerreviewed = {Yes}, title = {{Horizon} entropy with loop quantum gravity methods}, volume = {746}, year = {2015} } @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} } @misc{faucris.111921524, author = {Liegener, Klaus and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Hamiltonian} {Constraint} in {Loop} {Quantum} {Gravity}}, year = {2012} } @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} } @article{faucris.122513424, abstract = {These results can be extended to all polynomials of elementary operators and to a certain non-polynomial function of the elementary operators associated with the volume operator of quantum general relativity. These findings are another step towards establishing that the infinitesimal quantum dynamics of quantum general relativity might, to lowest order in (h) over bar, indeed be given by classical general relativity.}, author = {Thiemann, Thomas and Winkler, Oliver}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {4629-4681}, peerreviewed = {Yes}, title = {{Gauge} field theory coherent states ({GCS}): {III}. {Ehrenfest} theorems}, volume = {18}, year = {2001} } @masterthesis{faucris.108049744, abstract = {The dynamical laws of an evolving system determine how the system will look at later times, given some initial state the system started from. In quantum cosmology, one ap- plies this idea to the earliest moments of the universe, which requires one to have some idea about the intial conditions at the beginning of time. One proposal describing these initial conditions in the context of canonical quantum gravity is due to Hartle and Hawk- ing. Their proposal entails a preferred initial state for the universe which is based on a Euclidean path integral over all compact positive definite four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the constraint equations of general relativity in ADM variables in a formal sense.

}, author = {Frembs, Markus and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{The} holonomy-flux algebra in low dimensions}, year = {2013} } @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.109990364, abstract = {A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and spacetime topologies R-1 x R-1 and R-1 x S-1. (For the U(1) theory, we also consider the S-1 x S-1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed, These axioms are satisfied in the present model. (C) 1997 American Institute of Physics.}, author = {Ashtekar, Abhay and Lewandowski, Jerzy and Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas}, faupublication = {no}, journal = {Journal of Mathematical Physics}, pages = {5453-5482}, peerreviewed = {Yes}, title = {{SU}({N}) quantum {Yang}-{Mills} theory in two dimensions: {A} complete solution}, volume = {38}, year = {1997} } @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} } @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.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} } @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.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.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.123221384, abstract = {They turn out, as expected, to be non-local and form naturally a set of countable cardinality.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, month = {Jan}, pages = {59-88}, peerreviewed = {Yes}, title = {{COMPLETE} {QUANTIZATION} {OF} {A} {DIFFEOMORPHISM} {INVARIANT} {FIELD}-{THEORY}}, volume = {12}, year = {1995} } @misc{faucris.118832824, author = {Lohberger, Johannes and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Doubly} special relativity}, year = {2014} } @masterthesis{faucris.122308384, author = {Thurn, Andreas and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Constraint} {Analysis} of the {D}+1 dimensional {Palatini} action}, year = {2009} } @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.119253244, author = {Zilker, Thomas and Giesel, Kristina}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Manifestly} {Gauge} {Invariant} {Cosmological} {Perturbation} {Theory}}, year = {2013} } @article{faucris.115339224, abstract = {In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling back, the quantized bulk degrees of freedom. This is not yet fully realized in the-otherwise very successful-quantization of isolated horizons in loop quantum gravity. In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. There is no need to quantize them separately. We present evidence that for a horizon of sphere topology, the resulting horizon theory is remarkably similar to what has been found before. © 2011 American Physical Society.}, author = {Sahlmann, Hanno}, doi = {10.1103/PhysRevD.84.044049}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, keywords = {black holes; quantum gravity; horizons; loop quantum gravity}, peerreviewed = {Yes}, title = {{Black} hole horizons from within loop quantum gravity}, volume = {84}, year = {2011} } @article{faucris.120127084, abstract = {Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve. (C) 1999 American Institute of Physics. [S0022-2488(99)00404-1].}, author = {Mourao, José Manuel and Thiemann, Thomas and Velhinho, Jose}, faupublication = {no}, journal = {Journal of Mathematical Physics}, pages = {2337-2353}, peerreviewed = {Yes}, title = {{Physical} properties of quantum field theory measures}, volume = {40}, year = {1999} } @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.123698124, abstract = {This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain ''superselection laws'' that arise in current applications of these techniques to solving the diffeomorphism constraint are considered, Their status is elucidated by studying an analogous system: 2 + 1 Euclidean gravity, For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The usual quantum theory may still be obtained from a loop representation and the technique known as ''Refined Algebraic Quantization.'' (C) 1997 American Institute of Physics.}, author = {Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas}, faupublication = {no}, journal = {Journal of Mathematical Physics}, pages = {4730-4740}, peerreviewed = {Yes}, title = {{The} status of diffeomorphism superselection in euclidean 2+1 gravity}, volume = {38}, year = {1997} }