},
author = {Frembs, Markus and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{The} holonomy-flux algebra in low dimensions},
year = {2013}
}
@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}
}
@article{faucris.123560184,
abstract = {The Duflo map is a valuable tool for operator ordering in contexts in which Kirillov-Kostant brackets and their quantizations play a role. A priori, the Duflo map is only defined on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. Here we discuss extensions to the whole symmetric algebra, as well as their application to the calculation of Chern-Simons theory expectation values.},
author = {Sahlmann, Hanno and Zilker, Thomas},
doi = {10.1016/j.geomphys.2017.07.022},
faupublication = {yes},
journal = {Journal of Geometry and Physics},
pages = {297 - 308},
peerreviewed = {Yes},
title = {{Extensions} of the {Duflo} map and {Chern}-{Simons} expectation values},
volume = {121},
year = {2017}
}
@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.122381644,
abstract = {In this work we focus on the quantum Einstein-Yang-Mills sector quantized by the methods of loop quantum gravity. We point out the improved UV behavior of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact with the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relationship of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.},
author = {Liegener, Klaus and Thiemann, Thomas},
doi = {10.1103/PhysRevD.94.024042},
faupublication = {yes},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
peerreviewed = {unknown},
title = {{Towards} the fundamental spectrum of the quantum {Yang}-{Mills} theory},
volume = {94},
year = {2016}
}
@misc{faucris.111477124,
author = {Roelcke, Carmen and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Conical} space-time defects and their phenomenological consequences},
year = {2015}
}
@article{faucris.110370964,
abstract = {This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields). Published by AIP Publishing.},
author = {Stottmeister, Alexander and Thiemann, Thomas},
doi = {10.1063/1.4954228},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Coherent} states, quantum gravity, and the {Born}-{Oppenheimer} approximation. {I}. {General} considerations},
volume = {57},
year = {2016}
}
@article{faucris.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.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.

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.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.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}
}
@misc{faucris.111921524,
author = {Liegener, Klaus and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Hamiltonian} {Constraint} in {Loop} {Quantum} {Gravity}},
year = {2012}
}
@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.123831664,
abstract = {In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasized frequently. This idea has been picked up more recently in loop quantum gravity with the aim to perform a reduced phase space quantization of the theory, thus possibly avoiding problems with the (Dirac) operator constraint quantization method for a constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrize the space of theories considered so far. We then describe the quantum theory of a model that, to the best of our knowledge, has only been considered classically so far. This model could arguably be called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian, while at the same time reducing all constraints of general relativity.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/32/13/135015},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {scalar material reference systems;loop quantum gravity;Dirac observables},
peerreviewed = {Yes},
title = {{Scalar} material reference systems and loop quantum gravity},
volume = {32},
year = {2015}
}
@article{faucris.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}
}
@masterthesis{faucris.121937244,
author = {Reichert, Thorsten and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Quantum} {Mechanics} in the {Polymer} {Particle} {Representation}},
year = {2013}
}
@article{faucris.109133904,
abstract = {In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically coupled observer. the evolution of those observables is governed by a physical Hamiltonian and we derived the corresponding equations of motion. Linear perturbation theory of those equations of motion around a general exact solution in terms of manifestly gauge-invariant perturbations was then developed. In this paper we specialize our previous results to an FRW background which is also a solution of our modified equations of motion. We then compare the resulting equations with those derived in standard cosmological perturbation theory (SCPT). We exhibit the precise relation between our manifestly gauge-invariant perturbations and the linearly gauge-invariant variables in SCPT. We find that our equations of motion can be cast into SCPT form plus corrections. These corrections are the trace that the dust leaves on the system in terms of a conserved energy-momentum current density. In turns out that these corrections decay; in fact, in the late universe they are negligible whatever the value of the conserved current. We conclude that the addition of dust which serves as a test observer medium, while implying modifications of Einstein's equations without dust, leads to acceptable agreement with known results, while having the advantage that one now talks about manifestly gauge-invariant, that is measurable, quantities, which can be used even in perturbation theory at higher orders.},
author = {Giesel, Kristina and Hofmann, Stefan and Thiemann, Thomas and Winkler, Oliver},
doi = {10.1088/0264-9381/27/5/055006},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Manifestly} gauge-invariant general relativistic perturbation theory: {II}. {FRW} background and first order},
volume = {27},
year = {2010}
}
@article{faucris.110411004,
abstract = {This is the second paper concerning gauge-invariant coherent states for loop quantum gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the Abelian U(1) case encountered in the previous article (Class. Quantum Grav. 26 045011). We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss peaked in gauge- invariant quantities, as long as states are not labeled by degenerate gauge orbits, i.e. points where the gauge- invariant configuration space has singularities. In these cases the overlaps are still concentrated around these points, but the peak profile exhibits a plateau structure. This shows how the semiclassical properties of the states are influenced by the geometry of the gauge-invariant phase space.},
author = {Bahr, Benjamin and Thiemann, Thomas},
doi = {10.1088/0264-9381/26/4/045012},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Gauge}-invariant coherent states for loop quantum gravity: {II}. {Non}-{Abelian} gauge groups},
volume = {26},
year = {2009}
}
@article{faucris.123223804,
abstract = {After discussing the formalism at the classical level in a first paper (Lanery, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanery, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okolow (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanky, 2016, subsection 2.2) [1]. (C) 2017 Elsevier B.V. All rights reserved.},
author = {Lanery, Suzanne and Thiemann, Thomas},
doi = {10.1016/j.geomphys.2017.01.011},
faupublication = {yes},
journal = {Journal of Geometry and Physics},
keywords = {Quantum field theory;Projective limits;Algebras of observables;Geometric quantization;Position representation;Holomorphic quantization},
pages = {10-51},
peerreviewed = {Yes},
title = {{Projective} limits of state spaces {II}. {Quantum} formalism},
volume = {116},
year = {2017}
}
@article{faucris.123226884,
abstract = {The volume operator plays a crucial role in the definition of the quantum dynamics Of loop quantum gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only if one has sufficient control over the Volume spectrum. While closed formulae for the matrix elements are currently available in the literature, these are complicated polynomials in 6j symbols which ill turn are given in terms of Racah's formula which is too complicated in order to perform even numerical calculations for the semiclassically important regime of large spins. Hence, so far Hot even numerically the spectrum could be accessed. In this paper, we demonstrate that by means of the Elliot-Biedenharn identify one can get rid of all the 6j symbols for any valence of: the gauge-invariant vertex, thus immensely reducing the computational effort. We use the resulting compact formula to study numerically the spectrum of the gauge-invariant 4-vertex. The techniques derived in this paper-could also be of use for the analysis of spin-spin interaction Hamiltonians of many-particle problems in atomic and nuclear physics.},
author = {Brunnemann, Johannes and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/4/014},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1289-1346},
peerreviewed = {Yes},
title = {{Simplification} of the spectral analysis of the volume operator in loop quantum gravity},
volume = {23},
year = {2006}
}
@masterthesis{faucris.106243324,
author = {Davygora, Yuriy and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Kanonische} {Formulierung} der {Gravitationstheorien}},
year = {2009}
}
@article{faucris.110409904,
abstract = {In this paper, we investigate the properties of gauge-invariant coherent states for loop quantum gravity, for the gauge group U(1). This is done by projecting the corresponding complexifier coherent states defined by Thiemann and Winklerto the gauge- invariant Hilbert space. This being the first step toward constructing physical coherent states, we arrive at a set of gauge- invariant states that approximate well the gauge-invariant degrees of freedom of Abelian loop quantum gravity (LQG). Furthermore, these states turn out to encode explicit information about the graph topology, and show the same pleasant peakedness properties known from the gauge-variant complexifier coherent states. In a companion paper, we will turn to the more sophisticated case of SU(2).},
author = {Bahr, Benjamin and Thiemann, Thomas},
doi = {10.1088/0264-9381/26/4/045011},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Gauge}-invariant coherent states for loop quantum gravity: {I}. {Abelian} gauge groups},
volume = {26},
year = {2009}
}
@article{faucris.120859904,
abstract = {The volume operator plays a pivotal role for the quantum dynamics of loop quantum gravity (LQG). It is essential to construct triad operators that enter the Hamiltonian constraint and which become densely defined operators on the full Hilbert space, even though in the classical theory the triad becomes singular when classical GR breaks down. The expression for the volume and triad operators derives from the quantization of the fundamental electric flux operator of LQG by a complicated regularization procedure. In fact, there are two inequivalent volume operators available in the literature and, moreover, both operators are unique only up to a finite, multiplicative constant which should be viewed as a regularization ambiguity. Now on the one hand, classical volumes and triads can be expressed directly in terms of fluxes and this fact was used to construct the corresponding volume and triad operators. On the other hand, fluxes can be expressed in terms of triads and triads can be replaced by Poisson brackets between the holonomy and the volume operators. Therefore one can also view the holonomy operators and the volume operator as fundamental and consider the flux operator as a derived operator. In this paper we mathematically implement this second point of view and thus can examine whether the volume, triad and flux quantizations are consistent with each other. The results of this consistency analysis are rather surprising. Among other findings we show the following. ( 1) The regularization constant can be uniquely fixed. ( 2) One of the volume operators can be ruled out as inconsistent. ( 3) Factor ordering ambiguities in the definition of triad operators are immaterial for the classical limit of the derived flux operator. The results of this paper show that within full LQG triad operators are consistently quantized.},
author = {Giesel, Kristina and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/18/011},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {5667-5691},
peerreviewed = {Yes},
title = {{Consistency} check on volume and triad operator quantization in loop quantum gravity: {I}},
volume = {23},
year = {2006}
}
@article{faucris.224172763,
abstract = {Spin foam models (SFMs) are covariant formulations of loop quantum gravity (LQG) in four dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying the Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity can arise as a low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter delta becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.},
author = {Han, Muxin and Huang, Zichang and Zipfel, Antonia},
doi = {10.1103/PhysRevD.100.024060},
faupublication = {yes},
journal = {Physical Review D},
note = {CRIS-Team WoS Importer:2019-08-09},
peerreviewed = {Yes},
title = {{Emergent} four-dimensional linearized gravity from a spin foam model},
volume = {100},
year = {2019}
}
@article{faucris.120515604,
abstract = {In a remarkable paper (Koslowski T A 2007 arXiv:0709.3465[gr-qc]), Koslowski introduced kinematical representations for loop quantum gravity in which a non-degenerate spatial background metric is present. He also considered their properties and showed that Gauß and diffeomorphism constraints can be implemented. With this paper, we streamline and extend his treatment. In particular, we show that the standard regularization of the geometric operators leads to well-defined operators in the new representations, and we work out their properties fully. We also give details on the implementation of the constraints. All of this is done in such a way as to show that the standard representation is a particular (and in some ways exceptional) case of the more general constructions. This does not mean that these new representations are as fundamental as the standard one. Rather, we believe they might be useful to find some form of effective theory of loop quantum gravity on large scales. © 2010 IOP Publishing Ltd.},
author = {Sahlmann, Hanno},
doi = {10.1088/0264-9381/27/22/225007},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{On} loop quantum gravity kinematics with a non-degenerate spatial background},
volume = {27},
year = {2010}
}
@article{faucris.115376844,
abstract = {Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic lattice. We use this to calculate the lowest order coefficients of the dispersion relation for a specific one-dimensional model. © 2010 The American Physical Society.},
author = {Sahlmann, Hanno},
doi = {10.1103/PhysRevD.82.064018},
faupublication = {no},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
peerreviewed = {Yes},
title = {{Wave} propagation on a random lattice},
volume = {82},
year = {2010}
}
@article{faucris.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.201147872,
abstract = {We study the asymptotic behaviour of the vertex amplitude for the EPRL spin foam model extended to include timelike tetrahedra. We analyze both, tetrahedra of signature --- (standard EPRL), as well as of signature +-- (Hnybida-Conrady extension), in a unified fashion. However, we assume all faces to be of signature --. We find that the critical points of the extended model are described again by 4-simplices and the phase of the amplitude is equal to the Regge action. Interestingly, in addition to the Lorentzian and Euclidean sectors there appear also split signature 4-simplices.},
author = {Sahlmann, Hanno and Kaminski, Wojciech and Kisielowski, Marcin},
doi = {10.1088/1361-6382/aac6a4},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {quantum gravity;spin foam;EPRL model;stationary phase analysis;large spin limit},
peerreviewed = {Yes},
title = {{Asymptotic} analysis of the {EPRL} model with timelike tetrahedra},
volume = {35},
year = {2018}
}
@article{faucris.224377481,
author = {Bahr, Benjamin and Cunningham, William J. and Dittrich, Bianca and Glaser, Lisa and Lang, Dustin and Schnetter, Erik and Steinhaus, Sebastian},
doi = {10.1038/s41567-019-0626-1},
faupublication = {yes},
journal = {Nature Physics},
note = {CRIS-Team WoS Importer:2019-08-13},
pages = {724-725},
peerreviewed = {No},
title = {{Data} on sharing data},
volume = {15},
year = {2019}
}
@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.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.120317604,
abstract = {Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolow, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states. Published by AIP Publishing.},
author = {Lanery, Suzanne and Thiemann, Thomas},
doi = {10.1063/1.4968205},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Projective} loop quantum gravity. {I}. {State} space},
volume = {57},
year = {2016}
}
@article{faucris.217462920,
abstract = {The large-j asymptotic behavior of the four-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large-j asymptotic behavior is determined by the critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are asymptotic phases, whose exponents equal the Regge action of gravity. The amplitude may also contains critical configurations corresponding to nondegenerate split signature 4-simplices and degenerate vector geometries. But vertex amplitudes containing at least one timelike and one spacelike tetrahedra only give Lorentzian 4-simplices, while the split signature or degenerate 4-simplex does not appear.},
author = {Liu, Hongguang and Han, Muxin},
doi = {10.1103/PhysRevD.99.084040},
faupublication = {yes},
journal = {Physical Review D},
note = {CRIS-Team Scopus Importer:2019-05-14},
peerreviewed = {Yes},
title = {{Asymptotic} analysis of spin foam amplitude with timelike triangles},
volume = {99},
year = {2019}
}
@article{faucris.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.123505404,
abstract = {In this paper, we study the no-boundary wavefunction in scalartensor gravity with various potentials for the non-minimally coupled scalar field. Our goal is to calculate probabilities for the scalar fieldand hence the effective gravitational coupling and cosmological constantto take specific values. Most calculations are performed in the minisuperspace approximation, and we use a saddle point approximation for the Euclidean action, which is then evaluated numerically. We find that for potentials that have several minima, none of them is substantially preferred by the quantum-mechanical probabilities. We argue that the same is true for the stable and the runaway solution in the case of a dilaton-type potential. Technically, this is due to the inclusion of quantum-mechanical effects (fuzzy instantons). These results are in contrast to the often-held view that vanishing gravitation or cosmological constants would be exponentially preferred in quantum cosmology, and they may be relevant to the cosmological constant problem and the dilaton stabilization problem. © 2012 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Yeom, Dong-han and Hwang, Dong-il},
doi = {10.1088/0264-9381/29/9/095005},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{The} no-boundary measure in scalar-tensor gravity},
volume = {29},
year = {2012}
}
@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}
}
@article{faucris.217464944,
abstract = {We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved technically by combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for the one-particle excitations in the high-field quantum paramagnet. We find that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents. In the frustrated case on the square lattice the system remains in the universality class of the nearest-neighbor model independent of the long-range nature of the interaction, while we argue that the quantum criticality for the triangular lattice is terminated by a first-order phase transition line.},
author = {Fey, Sebastian and Kapfer, Sebastian and Schmidt, Kai Phillip},
doi = {10.1103/PhysRevLett.122.017203},
faupublication = {yes},
journal = {Physical Review Letters},
month = {Jan},
note = {CRIS-Team Scopus Importer:2019-05-14},
peerreviewed = {Yes},
title = {{Quantum} {Criticality} of {Two}-{Dimensional} {Quantum} {Magnets} with {Long}-{Range} {Interactions}},
volume = {122},
year = {2019}
}
@book{faucris.109463244,
abstract = {This volume presents a snapshot of the state-of-the-art in loop quantum gravity from the perspective of younger leading researchers. It takes the reader from the basics to recent advances, thereby bridging an important gap.

The aim is two-fold — to provide a contemporary introduction to the entire field for students and post-docs, and to present an overview of the current status for more senior researchers. The contributions include the latest developments that are not discussed in existing books, particularly recent advances in quantum dynamics both in the Hamiltonian and sum over histories approaches; and applications to cosmology of the early universe and to the quantum aspects of black holes.}, author = {Giesel, Kristina and Laddha, Alok and Varadarajan, Madhavan and Bianchi, Eugenio and Oriti, Daniele and Dittrich, Biancha and Agullo, Ivan and Singh, Parampreet and Fernando, Barbero and Perez, Alejandro and Barrau, Aurilien and Grain, Julien}, edition = {1}, editor = {Abhay A, Pullin, J}, faupublication = {yes}, isbn = {978-981-3209-92-3}, peerreviewed = {Yes}, publisher = {World Scientific}, series = {100 Years of General Relativity.}, title = {{Loop} {Quantum} {Gravity}. {The} first 30 years.}, volume = {4}, year = {2017} } @article{faucris.123480104, abstract = {We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single master constraint operator. While AQG is inspired by loop quantum gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of general relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken. There simply is no lattice regulator that must be sent to zero.}, author = {Giesel, Kristina and Thiemann, Thomas}, doi = {10.1088/0264-9381/24/10/003}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2465-2497}, peerreviewed = {Yes}, title = {{Algebraic} quantum gravity ({AQG}): {I}. {Conceptual} setup}, volume = {24}, year = {2007} } @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.

-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.120553004,
abstract = {Loop quantum cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of loop quantum gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical general relativity to spatially homogeneous situations which is then quantized by the methods of LQG. Thus, LQC is a quantum-mechanical toy model (finite number of degrees of freedom) for LQG (a genuine QFT with an infinite number of degrees of freedom) which provides important consistency checks. However, it is a non-trivial question whether the predictions of LQC are robust after switching on the inhomogeneous fluctuations present in full LQG. Two of the most spectacular findings of LQC are that: (1) the inverse scale factor is bounded from above on zero-volume eigenstates which hints at the avoidance of the local Curvature singularity and (2) the quantum Einstein equations are non-singular which hints at the avoidance of the global initial singularity. This rests on (1) a key technique developed for LQG and (2) the fact that there are no inhomogeneous excitations. We display the result of a calculation for LQG which proves that the (analogon of the) inverse scale factor, while densely defined, is not bounded from above on zero-volume eigenstates. Thus, in full LQG, if curvature singularity avoidance is realized, then not in this simple way. In fact, it turns out that the boundedness of the inverse scale factor is neither necessary nor sufficient for the curvature singularity avoidance and that non-singular evolution equations are neither necessary nor sufficient for initial singularity avoidance because none of these criteria are formulated in terms of observable quantities. After outlining what would be required, we present the results of a calculation for LQG which could be a first indication that our criteria at least for curvature singularity avoidance are satisfied in LQG.},
author = {Thiemann, Thomas and Brunnemann, Johannes},
doi = {10.1088/0264-9381/223/5/001},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1395-1427},
peerreviewed = {Yes},
title = {{On} (cosmological) singularity avoidance in loop quantum gravity},
volume = {23},
year = {2006}
}
@article{faucris.110341924,
abstract = {Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor-valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non-equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores.},
author = {Schröder-Turk, Gerd and Kapfer, Sebastian and Breidenbach, B. and Beisbart, C. and Mecke, Klaus},
doi = {10.1111/j.1365-2818.2009.03331.x},
faupublication = {yes},
journal = {Journal of Microscopy},
keywords = {Anisotropy;integral geometry;microstructured and cellular;materials;Minkowski functionals;morphology;strain and deformation;Turing patterns},
pages = {57-74},
peerreviewed = {Yes},
title = {{Tensorial} {Minkowski} functionals and anisotropy measures for planar patterns},
volume = {238},
year = {2010}
}
@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}
}
@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}
}
@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.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}
}
@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.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.200751890,
abstract = {Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to quantum cosmology with admissible ultraviolet behaviors leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. The evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in the quantum cosmology loop, eg as a natural instant of time to set initial conditions for the perturbations, so we analyze the positivity of the time-dependent mass when this bounce occurs. While the mass of the tensor perturbations is positive in the hybrid approach, the kinetic contribution to the energy density of the inflation dominates over its potential, as well as to a large area of the situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, it is becoming negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflation.

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.

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.123228644,
abstract = {This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein-Yang-Mills theory and 2+1 gravity. Interestingly, while Yang-Mills theory in 4D is not yet rigorously defined as ail ordinary (Wightman) quantum field theory oil Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss Constraint the master constraint can be solved explicitly, for the 2+1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by Only using spectral methods is as complicated as for 3+1 gravity and we therefore leave the complete analysis for 3+1 gravity.},
author = {Dittrich, Bianca and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/4/005},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1143-1162},
peerreviewed = {Yes},
title = {{Testing} the master constraint programme for loop quantum gravity: {V}. {Interacting} field theories},
volume = {23},
year = {2006}
}
@article{faucris.110414744,
abstract = {We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv: 1105.3703 [gr-qc]; arXiv: 1105.3704 [gr-qc]; arXiv: 1105.3705 [gr-qc]) to derive a connection formulation of Lorentzian general relativity coupled to Dirac fermions in dimensions D + 1 >= 3 with a compact gauge group. The technique that accomplishes that is similar to the one that has been introduced in 3+1 dimensions already. First one performs a canonical analysis of Lorentzian general relativity using the time gauge and then introduces an extension of the phase space analogous to the one employed in [1] to obtain a connection theory with SO(D + 1) as the internal gauge group subject to additional constraints. The success of this method rests heavily on the strong similarity of the Lorentzian and Euclidean Clifford algebras. A quantization of the Hamiltonian constraint is provided.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045004},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {IV}. {Matter} coupling},
volume = {30},
year = {2013}
}
@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.108974844,
abstract = {We give a brief introduction to Dirac observables and review the general construction of such Dirac observables for constrained systems in the framework of the Relational Formalism introduced by Rovelli(1) and further mathematically developed by Dittrich.(2) Finally we birefly discuss appropriate clocks for General Relativity and the evolution of observables generated by a so called physical Hamiltonian.},
author = {Giesel, Kristina},
doi = {10.1142/S0217751X08040056},
faupublication = {no},
journal = {International Journal of Modern Physics A},
pages = {1190-1199},
peerreviewed = {Yes},
title = {{Introduction} to {Dirac} observables},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0217751X08040056},
volume = {23},
year = {2008}
}
@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.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.

},
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.115336364,
abstract = {Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes' theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions.The abelian theory considered in the present article is the test case for our method. It can also be applied to the non-abelian theory. Results will be reported in a companion article. © 2011 Elsevier B.V.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1016/j.geomphys.2011.10.012},
faupublication = {yes},
journal = {Journal of Geometry and Physics},
keywords = {Abelian Chern-Simons theory; Generalized connections; Loop quantum gravity},
pages = {204-212},
peerreviewed = {Yes},
title = {{Abelian} {Chern}-{Simons} theory, {Stokes}' theorem, and generalized connections},
volume = {62},
year = {2012}
}
@article{faucris.120782464,
abstract = {In this article, we investigate the assumption of equipartition of energy in arguments for the entropic nature of gravity. It has already been pointed out by other authors that equipartition is not valid for low temperatures. Here we additionally point out that it is similarly not valid for systems with bounded energy. Many explanations for black hole entropy suggest that the microscopic systems responsible have a finite dimensional state space, and thus finite maximum energy. Assuming this to be the case leads to drastic corrections to Newton's law for high gravitational fields, and, in particular, to a singularity in acceleration at finite radius away from a point mass. This is suggestive of the physics at the Schwarzschild radius. We show, however, that the location of the singularity scales differently. © 2011 American Physical Society.},
author = {Sahlmann, Hanno},
doi = {10.1103/PhysRevD.84.104010},
faupublication = {no},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
peerreviewed = {Yes},
title = {{Energy} equipartition and minimal radius in entropic gravity},
volume = {84},
year = {2011}
}
@article{faucris.223560390,
abstract = {We perform a reduced phase space quantization of gravity using four Klein-Gordon scalar fields as reference matter as an alternative to the Brown-Kuchar dust model in Giesel and Thiemann (2010 Class. Quantum Grav. 27 175009), where dust scalar fields are used. We compare our results to an earlier model by Domagala et al (2010 Phys. Rev. D 82 104038) where only one Klein-Gordon scalar field is considered as reference matter for the Hamiltonian constraint but the spatial diffeomorphism constraints are quantized using Dirac quantization. As a result we find that the choice of four conventional Klein-Gordon scalar fields as reference matter leads to a reduced dynamical model that cannot be quantized using loop quantum gravity techniques. However, we further discuss a slight generalization of the action for the four Klein-Gordon scalar fields and show that this leads to a model which can be quantized in the framework of loop quantum gravity. By comparison of the physical Hamiltonian operators obtained from the model by Domagala et al (2010 Phys. Rev. D 82 104038) and the one introduced in this work we are able to make a first step towards comparing Dirac and reduced phase space quantization in the context of the spatial diffeomorphism constraints.},
author = {Giesel, Kristina and Vetter, Almut},
doi = {10.1088/1361-6382/ab26f4},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {Dirac observables; loop quantum gravity; reduced phase space quantization},
note = {CRIS-Team Scopus Importer:2019-08-02},
peerreviewed = {Yes},
title = {{Reduced} loop quantization with four {Klein}-{Gordon} scalar fields as reference matter},
volume = {36},
year = {2019}
}
@article{faucris.123506064,
abstract = {The present paper is the companion of Sahlmann and Thiemann (2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867) in which we proposed a scheme that tries to derive the quantum field theory (QFT) on curved spacetimes (CST) limit from background-independent quantum general relativity (QGR). The constructions of the companion paper make heavy use of the notion of semiclassical states for QGR. In the present paper, we employ the complexifier coherent states for QGR recently proposed by Thiemann and Winkler as semiclassical states, and thus fill the general formulae obtained in the companion paper with life. We demonstrate how one can, under some simplifying assumptions, explicitly compute expectation values of the operators relevant for the gravity-matter Hamiltonians of the companion paper in the complexifier coherent states. These expectation values give rise to effective matter Hamiltonians on the background on which the gravitational coherent state is peaked and thus induce approximate notions of n-particle states and matter propagation on fluctuating spacetimes. We display the details for the scalar and the electromagnetic field. The effective theories exhibit two types of corrections as compared to the ordinary QFT on CST. The first is due to the quantum fluctuations of the gravitational field and the second arises from the fact that background independence forces both geometry and matter to propagate on a spacetime of the form , where γ is a (random) graph. Finally, we obtain explicit numerical predictions for non-standard dispersion relations for the scalar and the electromagnetic field. They should, however, not be taken too seriously, due to the many ambiguities in our scheme, the analysis of the physical significance of which has only begun. We show, however, that one can classify these ambiguities at least in broad terms. © 2006 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/3/020},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {909-954},
peerreviewed = {Yes},
title = {{Towards} the {QFT} on curved spacetime limit of {QGR}: {II}. {A} concrete implementation},
volume = {23},
year = {2006}
}
@article{faucris.217019385,
abstract = {In Regge calculus, the space–time manifold is approximated by certain abstract simplicial complex, called a pseudomanifold, and the metric is approximated by an assignment of a length to each 1-simplex. In this paper for each pseudomanifold, we construct a smooth manifold which we call a manifold with defects. This manifold emerges from the purely combinatorial simplicial complex as a result of gluing geometric realizations of its n-simplices followed by removing the simplices of dimension n- 2. The Regge geometry is encoded in a boundary data of a BF theory on this manifold. We consider an action functional which coincides with the standard BF action for suitably regular manifolds with defects and fields. We show that the action evaluated at solutions of the field equations satisfying certain boundary conditions coincides with an evaluation of the Regge action at Regge geometries defined by the boundary data. As a result, the degrees of freedom of Regge calculus are traded for discrete degrees of freedom of topological BF theory.},
author = {Kisielowski, Marcin},
doi = {10.1007/s00023-018-0747-6},
faupublication = {yes},
journal = {Annales Henri Poincaré},
note = {CRIS-Team Scopus Importer:2019-05-07},
pages = {1403-1437},
peerreviewed = {Yes},
title = {{Relation} {Between} {Regge} {Calculus} and {BF} {Theory} on {Manifolds} with {Defects}},
volume = {20},
year = {2019}
}
@article{faucris.115362764,
abstract = {Some years ago, Radzikowski has found a characterization of Hadamard states for scalar quantum fields on a four-dimensional globally hyperbolic spacetime in terms of a specific form of the wavefront set of their two-point functions (termed "wavefront set spectrum condition"), thereby initiating a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, we extend this important result on the equivalence of the wavefront set spectrum condition with the Hadamard condition from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance scaling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.},
author = {Sahlmann, Hanno and Verch, Rainer},
doi = {10.1142/S0129055X01001010},
faupublication = {no},
journal = {Reviews in Mathematical Physics},
pages = {1203-1246},
peerreviewed = {Yes},
title = {{Microlocal} spectrum condition and {Hadamard} form for vector-valued quantum fields in curved spacetime},
volume = {13},
year = {2001}
}
@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}
}
@inproceedings{faucris.123218084,
author = {Ashtekar, Abhay and Lewandowski, Jerzy and Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas},
faupublication = {no},
month = {Jan},
pages = {60-86},
peerreviewed = {unknown},
title = {{A} manifestly gauge-invariant approach to quantum theories of gauge fields},
year = {1995}
}
@article{faucris.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.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.123191244,
abstract = {Two-dimensional hard-particle systems are rather easy to simulate but surprisingly difficult to treat by theory. Despite their importance from both theoretical and experimental points of view, theoretical approaches are usually qualitative or at best semi-quantitative. Here, we present a density functional theory based on the ideas of fundamental measure theory for two-dimensional hard-disk mixtures, which allows for the first time an accurate description of the structure of the dense fluid and the equation of state for the solid phase within the framework of density functional theory. The properties of the solid phase are obtained by freely minimizing the functional. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3687921]},
author = {Roth, Roland and Mecke, Klaus and Oettel, Martin},
doi = {10.1063/1.3687921},
faupublication = {yes},
journal = {Journal of Chemical Physics},
keywords = {density functional theory;equations of state},
peerreviewed = {Yes},
title = {{Communication}: {Fundamental} measure theory for hard disks: {Fluid} and solid},
volume = {136},
year = {2012}
}
@article{faucris.123693064,
abstract = {This paper is the first in a series of seven papers with the title 'quantum spin dynamics (QSD)'.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {839-873},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD})},
volume = {15},
year = {1998}
}
@article{faucris.118959984,
abstract = {Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic observables of the theory, the Ashtekar-Isham-Lewandowski (AIL) representation, has been constructed. Recently, several uniqueness results for this representation have been worked out. In the present paper, we contribute to these efforts by showing that the AIL representation is irreducible, provided it is viewed as the representation of a certain C*-algebra which is very similar to the Weyl algebra used in the canonical quantization of free quantum field theories. © 2006 IOP Publishing Ltd.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1088/0264-9381/23/13/010},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {4453-4471},
peerreviewed = {Yes},
title = {{Irreducibility} of the {Ashtekar}-{Isham}-{Lewandowski} representation},
volume = {23},
year = {2006}
}
@article{faucris.122248544,
author = {Giesel, Kristina and Oelmann, Almut},
faupublication = {yes},
journal = {Acta Physica Polonica B},
pages = {339-349},
peerreviewed = {Yes},
title = {{Comparison} {Between} {Dirac} and {Reduced} {Quantization} in {LQG}-{Models} with {Klein}-{Gordon} {Scalar} {Fields}},
volume = {Acta Phys.Polon.Supp.},
year = {2017}
}
@article{faucris.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}
}
@misc{faucris.120250284,
author = {Sahlmann, Hanno and Wolz, Florian},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Geometric} meaning of the {Penrose} metric},
year = {2014}
}
@article{faucris.123835184,
abstract = {Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e. g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge-invariant degrees of freedom which allow unambiguous comparison between theory and experiment. When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to nth order in terms of quantities that are gauge-invariant up to terms of higher orders becomes highly non-trivial and cumbersome. This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature. In this series of papers we circumvent these difficulties by passing to a manifestly gauge-invariant framework. In other words, we only perturb gauge-invariant, i.e. measurable quantities, rather than gauge variant ones. Thus, gauge invariance is preserved non-perturbatively while we construct the perturbation theory for the equations of motion for the gauge-invariant observables to all orders. In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchar as well as the relational formalism due to Rovelli. In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order. As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment. However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge-invariant generalization to higher orders. This will also allow us to settle the stability issue in a future publication.},
author = {Giesel, Kristina and Hofmann, Stefan and Thiemann, Thomas and Winkler, Oliver},
doi = {10.1088/0264-9381/27/5/055005},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Manifestly} gauge-invariant general relativistic perturbation theory: {I}. {Foundations}},
volume = {27},
year = {2010}
}
@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.226555401,
abstract = {We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by identifying those variables for the description of the perturbations that display a dynamical behavior adapted in a specific way to the evolution of the entire cosmology. We make use of a canonical formulation of the whole of the cosmological system (background geometry and perturbations) in which the perturbative gauge-invariant degrees of freedom are identified as canonical variables. Introducing background-dependent linear canonical transformations that respect the spatial symmetries of the background on these perturbations and completing those canonical transformations for the entire system, we are able to characterize a generic collection of annihilation and creation like variables that obey the dynamics dictated by a respective collection of Hamiltonians. We then impose that such Hamiltonians possess no self-interaction terms so that, in a Fock representation with normal ordering, they act diagonally on the basis of n-particle states. This leads to a semilinear first-order partial differential equation with respect to the background for the coefficients that define the annihilation and creationlike variables for all Fourier modes, as well as to a very precise ultraviolet characterization of them. Such first-order equation contains, in the imaginary part of its complex solutions, the complicated second-order field equation that typically arises for the time-dependent frequency of the perturbations in the context of quantum field theory in curved spacetimes. We check that the asymptotic knowledge acquired allows one to select the standard vacua in Minkowski and de Sitter spacetimes. Finally, we discuss the relation of our vacuum and the standard adiabatic vacua, and check that our asymptotic characterization of variables with a diagonal Hamiltonian displays the properties that would be desirable for an adiabatic state of infinite order.},
author = {Navascues, Beatriz Elizaga and Mena Marugan, Guillermo A. and Thiemann, Thomas},
doi = {10.1088/1361-6382/ab32af},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
note = {CRIS-Team WoS Importer:2019-09-13},
peerreviewed = {Yes},
title = {{Hamiltonian} diagonalization in hybrid quantum cosmology},
volume = {36},
year = {2019}
}
@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.110418924,
abstract = {In the first paper of this series, an extension of the Ashtekar-Lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by Kijowski. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (also known as holonomies and fluxes). While this is the first step toward the construction of states semi-classical with respect to a full set of observables, one uncovers a deeper issue, which we analyse in the present article in the case of real-valued holonomies. Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomy and flux observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself. Away out would be to suitably restrict the algebra of observables: we take the first step in this direction in a companion paper. Published by AIP Publishing.},
author = {Lanery, Suzanne and Thiemann, Thomas},
doi = {10.1063/1.4983133},
faupublication = {yes},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{Projective} loop quantum gravity. {II}. {Searching} for semi-classical states},
volume = {58},
year = {2017}
}
@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}
}
@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.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.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.119297684,
abstract = {The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge invariant formalism is used to compute the evolution equations of linear perturbations around a general relativistic spacetime background in the Jordan frame. These equations are then specialized to the case of a flat FRW cosmological background. Furthermore, the equivalence between the Jordan frame and the Einstein frame of STT in the manifestly gauge invariant Hamiltonian formalism is analyzed, and it is shown that also in this framework they can be related by a conformal transformation. Finally, the obtained evolution equations for the linear perturbations in our formalism are compared with those in the standard cosmological perturbation theory. It turns out that the perturbation equations in the two different formalisms coincide with each other in a suitable limit.},
author = {Han, Yu and Giesel, Kristina and Ma, Yongge},
doi = {10.1088/0264-9381/32/13/135006},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
keywords = {scalar-tensor theories of gravity;cosmological perturbation theory;manifestly gauge invariant perturbations},
peerreviewed = {Yes},
title = {{Manifestly} gauge invariant perturbations of scalar-tensor theories of gravity},
volume = {32},
year = {2015}
}
@article{faucris.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.201148142,
abstract = {We describe the quantum theory of isolated horizons with electromagnetic or non-Abelian gauge charges in a setting in which both the gauge and gravitational field are quantized. We consider the distorted case, and its spherically symmetric limit. We show that the gravitational horizon d.o.f. give rise to the Bekenstein-Hawking relation, with lower-order terms giving some corrections for small black holes. We also demonstrate that one can include matter d.o.f. in the state counting. We show that one can expect (potentially divergent) contributions proportional to the area, as well as logarithmic corrections proportional to the horizon charge. This is qualitatively similar to results on matter contributions obtained with other methods in the literature.},
author = {Sahlmann, Hanno and Eder, Konstantin},
doi = {10.1103/PhysRevD.97.086016},
faupublication = {yes},
journal = {Physical Review D},
peerreviewed = {Yes},
title = {{Quantum} theory of charged isolated horizons},
volume = {97},
year = {2018}
}
@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.

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

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

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

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

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

}, author = {Wolz, Florian and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{On} spatially diffeomorphism invariant quantizations of the bosonic string}, year = {2015} } @article{faucris.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} } @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} } @misc{faucris.214360202, author = {Zwicknagel, Ernst-Albrecht and Giesel, Kristina and Liegener, Klaus}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Expectation} {Values} of {Holonomy}-{Operators} in {Cosmological} {Coherent} {States} for {Loop} {Quantum} {Gravity}}, year = {2018} } @article{faucris.115370684, abstract = {Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of (kinematical) observables and of a representation of A on a measure space over the space of generalized connections. This representation is singled out by its elegance and diffeomorphism covariance. Recently, in the context of the quest for semiclassical states, states of the theory in which the quantum gravitational field is close to some classical geometry, it was realized that it might also be worthwhile to study different representations of the algebra A. The content of the present work is the observation that under some mild assumptions, the mathematical structure of representations of A can be analyzed rather effortlessly, to a certain extent: each representation can be labeled by sets of functions and measures on the space of (generalized) connections that fulfill certain conditions. © 2011 American Institute of Physics.}, author = {Sahlmann, Hanno}, doi = {10.1063/1.3525705}, faupublication = {no}, journal = {Journal of Mathematical Physics}, peerreviewed = {Yes}, title = {{Some} results concerning the representation theory of the algebra underlying loop quantum gravity}, volume = {52}, year = {2011} } @article{faucris.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} } @misc{faucris.214359337, abstract = {

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.