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.

}, author = {Frembs, Markus and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{The} holonomy-flux algebra in low dimensions}, year = {2013} } @article{faucris.214173102, abstract = {A spin-foam model is derived from the canonical model of loop quantum gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of loop quantum cosmology by Ashtekar et al (2009 Phys. Len. B 681 347-52), later developed by Henderson et al (2011 Glass. Quantum Grav. 28 025003).}, author = {Kisielowski, Marcin and Lewandowski, Jerzy}, doi = {10.1088/1361-6382/aafcc0}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, note = {CRIS-Team WoS Importer:2019-03-22}, peerreviewed = {Yes}, title = {{Spin}-foam model for gravity coupled to massless scalar field}, volume = {36}, year = {2019} } @misc{faucris.111423664, author = {Zilker, Thomas and Thiemann, Thomas}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Quantum} {Simplicity} {Constraints} and {Area} {Spectrum}}, year = {2010} } @article{faucris.123505404, abstract = {In this paper, we study the no-boundary wavefunction in scalartensor gravity with various potentials for the non-minimally coupled scalar field. Our goal is to calculate probabilities for the scalar fieldand hence the effective gravitational coupling and cosmological constantto take specific values. Most calculations are performed in the minisuperspace approximation, and we use a saddle point approximation for the Euclidean action, which is then evaluated numerically. We find that for potentials that have several minima, none of them is substantially preferred by the quantum-mechanical probabilities. We argue that the same is true for the stable and the runaway solution in the case of a dilaton-type potential. Technically, this is due to the inclusion of quantum-mechanical effects (fuzzy instantons). These results are in contrast to the often-held view that vanishing gravitation or cosmological constants would be exponentially preferred in quantum cosmology, and they may be relevant to the cosmological constant problem and the dilaton stabilization problem. © 2012 IOP Publishing Ltd.}, author = {Sahlmann, Hanno and Yeom, Dong-han and Hwang, Dong-il}, doi = {10.1088/0264-9381/29/9/095005}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{The} no-boundary measure in scalar-tensor gravity}, volume = {29}, year = {2012} } @article{faucris.118263464, abstract = {Finally, we comment on the status of the Wick rotation transform in the light of the present results and give an intuitive description of the action of the Hamiltonian constraint.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {875-905}, peerreviewed = {Yes}, title = {{Quantum} spin dynamics ({QSD}): {II}. {The} kernel of the {Wheeler}-{DeWitt} constraint operator}, volume = {15}, year = {1998} } @article{faucris.123228864, abstract = {We combine (i) background-independent loop quantum gravity (LQG) quantization techniques, (ii) the mathematically rigorous framework of algebraic quantum field theory (AQFT) and (iii) the theory of integrable systems resulting in the invariant Pohlmeyer charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge, new, non-trivial solution to the representation problem. This solution exists (1) for any target space dimension, (2) for Minkowski signature of the target space, (3) without tachyons, (4) manifestly ghost free (no negative norm states), (5) without fixing a worldsheet or target space gauge, (6) without (Virasoro) anomalies (zero central charge), (7) while preserving manifest target space Poincare invariance and (8) without picking up UV divergences. The existence of this stable solution is, on one hand, exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. On the other hand, if such solutions are found, then this would prove that neither a critical dimension (D = 10, 11, 26) nor supersymmetry is a prediction of string theory. Rather, these would be features of the particular Fock representation of current string theory and hence would not be generic. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper, we treat the more complicated case of curved target spaces.}, author = {Thiemann, Thomas}, doi = {10.1088/0264-9381/23/6/007}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {1923-1970}, peerreviewed = {Yes}, title = {{The} {LQG} string - loop quantum gravity quantization of string theory: {I}. {Flat} target space}, volume = {23}, year = {2006} } @masterthesis{faucris.111021944, abstract = {Gaussian path integrals play an important role for free quantum field theories, and for the perturbative treatment of interacting quantum field theories. These path integrals are defined via measures on linear spaces. For loop quantum gravity, a framework for path integrals over spaces of connections was developed. Some examples of what one could call Gaussian measures are known. They are interesting, among other things, because they give the connections finite quantum mechanical fluctuations.

},
author = {Nekovar, Stefan and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Gaussian} {Measures} and {Representations} of the {Holonomy}-{Flux} {Algebra}},
year = {2014}
}
@article{faucris.122018424,
abstract = {It is shown - in Ashtekar's canonical framework of General Relativity - that spherically symmetric (Schwarzschild) gravity in four-dimensional space-time constitutes a finite-dimensional completely integrable system. Canonically conjugate observables for asymptotically flat spacetimes are masses as action variables and - surprisingly - time variables as angle variables, each of which is associated with an asymptotic ''end'' of the Cauchy surfaces. The emergence of the time observable is a consequence of the Hamiltonian formulation and its subtleties concerning the slicing of space and time and is not in contradiction to Birkhoff's theorem. The results are of interest as to the concept of time in General Relativity, They can be formulated within the ADM formalism, too. Quantization of the system and the associated Schrodinger equation depend on the allowed spectrum of the masses.},
author = {Kastrup, Hans and Thiemann, Thomas},
faupublication = {no},
journal = {Nuclear Physics B},
pages = {665-686},
peerreviewed = {Yes},
title = {{SPHERICALLY} {SYMMETRICAL} {GRAVITY} {AS} {A} {COMPLETELY} {INTEGRABLE} {SYSTEM}},
volume = {425},
year = {1994}
}
@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.123229524,
abstract = {Should nature be supersymmetric, then it will be described by Quantum Supergravity at least in some energy regimes. The currently most advanced description of Quantum Supergravity and beyond is Superstring Theory/M-Theory in 10/11 dimensions. String Theory is a top-to-bottom approach to Quantum Supergravity in that it postulates a new object, the string, from which classical Supergravity emerges as a low energy limit. On the other hand, one may try more traditional bottom-to-top routes and apply the techniques of Quantum Field Theory. Loop Quantum Gravity (LQG) is a manifestly background independent and non-perturbative approach to the quantisation of classical General Relativity, however, so far mostly without supersymmetry. The main obstacle to the extension of the techniques of LQG to the quantisation of higher dimensional Supergravity is that LQG rests on a specific connection formulation of General Relativity which exists only in D + 1 = 4 dimensions. In this Letter we introduce a new connection formulation of General Relativity which exists in all space-time dimensions. We show that all LQG techniques developed in D + 1 = 4 can be transferred to the new variables in all dimensions and describe how they can be generalised to the new types of fields that appear in Supergravity theories as compared to standard matter, specifically Rarita-Schwinger and p-form gauge fields. (C) 2012 Elsevier B.V. All rights reserved.},
author = {Bodendorfer, Norbert and Thurn, Andreas and Thiemann, Thomas},
doi = {10.1016/j.physletb.2012.04.003},
faupublication = {yes},
journal = {Physics Letters B},
keywords = {Loop quantum gravity;Supergravity;Higher dimensional gravity},
pages = {205-211},
peerreviewed = {Yes},
title = {{Towards} {Loop} {Quantum} {Supergravity} ({LQSG})},
volume = {711},
year = {2012}
}
@article{faucris.110372944,
abstract = {In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only a finite number of isolated intersections. This assumption implies a limitation on the diffeomorphisms invariance of the introduced structures. In this work, using the previous results of Baez and Sawin, we extend the existing results to a theory admitting all the possible piecewise-smooth finite paths and loops. In particular, we (a) characterize the spectrum of the Ashtekar-Isham configuration space, (b) introduce spin-web states, a generalization of the spin network states, (c) extend the diffeomorphism averaging to the spin-web states and derive a large class of diffeomorphism-invariant states and finally (d) extend the 3-geometry operators and the Hamiltonian operator.},
author = {Lewandowski, Jerzy and Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2299-2322},
peerreviewed = {Yes},
title = {{Diffeomorphism}-invariant quantum field theories of connections in terms of webs},
volume = {16},
year = {1999}
}
@article{faucris.215948807,
author = {Giesel, Kristina and Singh, Parampreet and Winnekens, David},
doi = {10.1088/1361-6382/ab0ed3},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
pages = {085009},
peerreviewed = {Yes},
title = {{Dynamics} of {Dirac} observables in canonical cosmological perturbation theory},
volume = {36},
year = {2019}
}
@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.118959324,
abstract = {We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and an su(2)-valued one-form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similarly to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.},
author = {Sahlmann, Hanno and Pranzetti, Daniele},
doi = {10.1016/j.physletb.2015.04.070},
faupublication = {yes},
journal = {Physics Letters B},
pages = {209-216},
peerreviewed = {Yes},
title = {{Horizon} entropy with loop quantum gravity methods},
volume = {746},
year = {2015}
}
@misc{faucris.111478004,
author = {Eder, Konstantin and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Quantum} tetrahedron and loop quantum gravity: {The} monochromatic four-vertex},
year = {2015}
}
@article{faucris.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.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.123222264,
abstract = {Most of the fermionic part of this work is independent of the recent preprint by Baez and Krasnov and earlier work by Rovelli and Morales-Tecotl because we use new canonical fermionic variables, so-called Grassman-valued half-densities, which enable us to solve the difficult fermionic adjointness relations.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1487-1512},
peerreviewed = {Yes},
title = {{Kinematical} {Hilbert} spaces for fermionic and {Higgs} quantum field theories},
volume = {15},
year = {1998}
}
@masterthesis{faucris.201058905,
author = {Wichert, Josef and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{The} ideas of {Kaluza} and {Klein} in the context of loop quantum gravity},
year = {2018}
}
@article{faucris.110403744,
abstract = {Spin-foam models are supposed to be discretized path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration is that no consensus has been reached for how to implement the simplicity constraints. Indeed, none of these models strictly follows from the original path integral with commuting B fields, rather, by some nonstandardmanipulations one always ends up with non-commuting B fields and the simplicity constraints become in fact anomalous which is the source for there being several inequivalent strategies to circumvent the associated problems. In this paper, we construct a new Euclidian spin-foam model which is constructed by standard methods from the Plebanski-Holst path integral with commuting B fields discretized on a 4D simplicial complex. The resulting model differs from the current ones in several aspects, one of them being that the closure constraint needs special care. Only when dropping the closure constraint by hand and only in the large spin limit can the vertex amplitudes of this model be related to those of the FK gamma. model but even then the face and edge amplitude differ. Interestingly, a non-commutative deformation of the B-IJ variables leads from our new model to the Barrett-Crane model in the case of gamma =infinity.},
author = {Han, Muxin and Thiemann, Thomas},
doi = {10.1088/0264-9381/30/23/235024},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Commuting} simplicity and closure constraints for {4D} spin-foam models},
volume = {30},
year = {2013}
}
@article{faucris.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}
}
@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.108346964,
abstract = {We quantize the new connection formulation of (D + 1)-dimensional general relativity developed in our companion papers by loop quantum gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalize to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its 'diagonal' components acting at edges of spin-network functions are easily solved, its 'off-diagonal' components acting at vertices are non-trivial and require a more elaborate treatment.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045003},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {III}. {Quantum} theory},
volume = {30},
year = {2013}
}
@article{faucris.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.110413644,
abstract = {Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one's disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauss, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045001},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{New} variables for classical and quantum gravity in all dimensions: {I}. {Hamiltonian} analysis},
volume = {30},
year = {2013}
}
@misc{faucris.111477124,
author = {Roelcke, Carmen and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Conical} space-time defects and their phenomenological consequences},
year = {2015}
}
@article{faucris.108971984,
abstract = {Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations which are predictive, interpretable, and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry: the latter must be hyperbolic, time-orientable, and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics-for the general tensorial spacetime geometries satisfying the above minimum requirements-is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus, the search for modified gravitational dynamics is reduced to a clear mathematical task.},
author = {Giesel, Kristina and Schuller, Frederic and Witte, Christof and Wolfarth, Matthias},
doi = {10.1103/PhysRevD.85.104042},
faupublication = {yes},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
peerreviewed = {Yes},
title = {{Gravitational} dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter},
volume = {85},
year = {2012}
}
@article{faucris.110421564,
abstract = {Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is designed to overcome the complications associated with the non-Lie-algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For the case of 3+1 gravity itself, so far only a positive quadratic form for the master constraint operator was derived. In this paper, we close this gap and prove that the quadratic form is closable and thus stems from a unique self-adjoint master constraint operator. The proof rests on a simple feature of the general pattern according to which Hamiltonian constraints in LQG are constructed and thus extends to arbitrary matter coupling and holds for any metric signature. With this result the existence of a physical Hilbert space for LQG is established by standard spectral analysis.},
author = {Thiemann, Thomas},
doi = {10.1088/0264-9381/23/7/003},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2249-2265},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics: {VIII}. {The} master constraint},
volume = {23},
year = {2006}
}
@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.

This thesis is devoted to the study of the quantum theory of charged black holes in the context of loop quantum gravity, extending the model of the quantum black hole as considered so far in the literature. We therefore consider Maxwell theory coupled to gravity de ned on a spacetime manifold with internal boundary described by an isolated horizon, construct the Hamiltonian formulation of the classical system, quantize the corresponding symplectic phase space and nally go over to the computation of the black hole entropy. We consider the spherically symmetric case in the U(1) framework as well as the distorted case following the SU(2) approach. The resulting picture depends signi cantly on the choices made for the quantization and the de nition of the state counting. We show that there is a choice such that the Bekenstein-Hawking relation holds. At the end, we use the theory in order to address the question whether there is a correspondence between the highly damped quasinormal modes and the area spectra of quantum charged black holes in the framework of loop quantum gravity. },
author = {Eder, Konstantin and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Quantum} theory of charged black hole horizons},
year = {2017}
}
@article{faucris.120127084,
abstract = {Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve. (C) 1999 American Institute of Physics. [S0022-2488(99)00404-1].},
author = {Mourao, José Manuel and Thiemann, Thomas and Velhinho, Jose},
faupublication = {no},
journal = {Journal of Mathematical Physics},
pages = {2337-2353},
peerreviewed = {Yes},
title = {{Physical} properties of quantum field theory measures},
volume = {40},
year = {1999}
}
@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.123698124,
abstract = {This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain ''superselection laws'' that arise in current applications of these techniques to solving the diffeomorphism constraint are considered, Their status is elucidated by studying an analogous system: 2 + 1 Euclidean gravity, For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The usual quantum theory may still be obtained from a loop representation and the technique known as ''Refined Algebraic Quantization.'' (C) 1997 American Institute of Physics.},
author = {Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas},
faupublication = {no},
journal = {Journal of Mathematical Physics},
pages = {4730-4740},
peerreviewed = {Yes},
title = {{The} status of diffeomorphism superselection in euclidean 2+1 gravity},
volume = {38},
year = {1997}
}
@article{faucris.115349784,
abstract = {We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Liealgebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups. © 2012 American Physical Society.},
author = {Sahlmann, Hanno and Thiemann, Thomas},
doi = {10.1103/PhysRevLett.108.111303},
faupublication = {yes},
journal = {Physical Review Letters},
peerreviewed = {Yes},
title = {{Chern}-simons expectation values and quantum horizons from loop quantum gravity and the duflo map},
volume = {108},
year = {2012}
}
@article{faucris.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}
}
@inproceedings{faucris.106209224,
abstract = {I will survey the formalism and main results of loop quantum gravity [1], [2] from a mathematical perspective. Then I take a closer look at the way black hole horizons are treated in the theory, by coupling a Chern-Simons theory on the horizon to the bulk degrees of freedom [3]. I will present some recent results on a new way to solve the self-duality equation involved directly in the quantum theory [4].},
author = {Sahlmann, Hanno},
doi = {10.1142/9789814449243_0075},
faupublication = {yes},
isbn = {9789814449236},
keywords = {Black holes; Duo isomorphism; Measures on spaces of connections; Quantum gravity; TQFT},
peerreviewed = {unknown},
publisher = {World Scientific Publishing Co.},
title = {{From} groups and knots to black hole entropy - mathematical aspects of loop quantum gravity},
year = {2013}
}
@article{faucris.123229964,
abstract = {In our companion paper, we focused on the quantization of the Rarita-Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime dimensions. In this paper, we extend this analysis by considering the quantization of additional bosonic fields necessary to obtain a complete SUSY multiplet next to graviton and gravitino in various dimensions. As a generic example, we study concretely the quantization of the 3-index photon of minimal 11d SUGRA, but our methods easily extend to more general p-form fields. Due to the presence of a Chern-Simons term for the 3-index photon, which is due to local SUSY, the theory is self-interacting and its quantization far from straightforward. Nevertheless, we show that a reduced phase space quantization with respect to the 3-index photon Gauss constraint is possible. Specifically, the Weyl algebra of observables, which deviates from the usual CCR Weyl algebras by an interesting twist contribution proportional to the level of the Chern-Simons theory, admits a background independent state of the Narnhofer-Thirring type.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045007},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Towards} loop quantum supergravity ({LQSG}): {II}. p-form sector},
volume = {30},
year = {2013}
}
@article{faucris.122507264,
abstract = {In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity.},
author = {Bahr, Benjamin and Thiemann, Thomas},
doi = {10.1088/0264-9381/24/8/011},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {2109-2138},
peerreviewed = {Yes},
title = {{Approximating} the physical inner product of loop quantum cosmology},
volume = {24},
year = {2007}
}
@misc{faucris.119643304,
author = {Zöbelein, Carolin and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Dirac}-{Observablen} in der {Kosmolgie}},
year = {2013}
}
@masterthesis{faucris.123268464,
author = {Bodendorfer, Norbert and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Canonical} {Analysis} of {Gravity} {Theories} without the {Time} {Gauge}},
year = {2009}
}
@article{faucris.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.122512324,
abstract = {Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantum field. In this paper, we extend that construction to more general theories which do not refer to any background, spacetime metric (and in which the space of histories does not admit a natural linear structure). Examples include certain gauge theories, topological field theories and relativistic gravitational theories. The treatment is self-contained in the sense that an a priori knowledge of the Osterwalder-Schrader theorem is not assumed.},
author = {Ashtekar, Abhay and Marolf, Donald and Mourao, José Manuel and Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {4919-4940},
peerreviewed = {Yes},
title = {{Constructing} {Hamiltonian} quantum theories from path integrals in a diffeomorphism-invariant context},
volume = {17},
year = {2000}
}
@misc{faucris.111490764,
author = {Reichert, Thorsten and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Angular} {Momentum} and {Quantum} {Gravity}},
year = {2010}
}
@article{faucris.110400884,
abstract = {One of the celebrated results of loop quantum gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area, and volume operators. This is an indication that the Planck scale geometry in LQG is discontinuous rather than smooth. However, there is no rigorous proof thereof at present. Because the aforementioned operators are not gauge invariant, they do not commute with the quantum constraints. The relational formalism in the incarnation of Rovelli's partial and complete observables provides a possible mechanism for turning a non-gauge-invariant operator into a gauge invariant one. In this paper we investigate whether the spectrum of such a physical, that is, gauge invariant, observable can be predicted from the spectrum of the corresponding gauge variant observables. We will not do this in full LQG but rather consider much simpler examples where field theoretical complications are absent. We find, even in those simpler cases, that kinematical discreteness of the spectrum does not necessarily survive at the gauge invariant level. Whether or not this happens depends crucially on how the gauge invariant completion is performed. This indicates that "fundamental discreteness at the Planck scale in LQG" is far from established. To prove it, one must provide the detailed construction of gauge invariant versions of geometrical operators.},
author = {Dittrich, Bianca and Thiemann, Thomas},
doi = {10.1063/1.3054277},
faupublication = {no},
journal = {Journal of Mathematical Physics},
keywords = {geometry;mathematical operators;quantum gravity},
month = {Jan},
peerreviewed = {Yes},
title = {{Are} the spectra of geometrical operators in loop quantum gravity really discrete?},
volume = {50},
year = {2009}
}
@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.107360264,
abstract = {The no-boundary wavefunction of quantum gravity usually assigns only very small probability to long periods of inflation. This was a reason to doubt about the no-boundary wavefunction to explain the observational universe. We study the no-boundary proposal in the context of multi-field inflation to see whether the number of fields changes the situation. For a simple model, we find that indeed the no-boundary wavefunction can give higher probability for sufficient inflation, but the number of fields involved N has to be very high, e.g., N ≃ m. © 2013 IOP Publishing Ltd.},
author = {Hwang, Dong-il and Kim, Soo A and Lee, Bum-Hoon and Sahlmann, Hanno and Yeom, Dong-han},
doi = {10.1088/0264-9381/30/16/165016},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{No}-boundary measure and preference for large e-foldings in multi-field inflation},
volume = {30},
year = {2013}
}
@article{faucris.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.

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}
}
@misc{faucris.214358865,
author = {Matas, Bystrik and Giesel, Kristina and Kobler, Michael},
faupublication = {yes},
peerreviewed = {automatic},
title = {{The} {Lewis}-{Riesenfeld} {Invariant} in the context of a {Loop} {Quantum} {Cosmology} quantisation},
year = {2018}
}
@article{faucris.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}
}
@masterthesis{faucris.112636744,
author = {Leitherer, Andreas and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{The} {Schrödinger} {Equation} of the {Gowdy} {Model} in {Reduced} {Algebraic} {Quantum} {Gravity}},
year = {2017}
}
@misc{faucris.111921524,
author = {Liegener, Klaus and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Hamiltonian} {Constraint} in {Loop} {Quantum} {Gravity}},
year = {2012}
}
@masterthesis{faucris.119253244,
author = {Zilker, Thomas and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Manifestly} {Gauge} {Invariant} {Cosmological} {Perturbation} {Theory}},
year = {2013}
}
@misc{faucris.201058655,
author = {Wichert, Josef and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{What} does the {Penrose} operator measure in loop quantum gravity?},
year = {2016}
}
@article{faucris.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}
}
@phdthesis{faucris.121044704,
author = {Thurn, Andreas and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Higher} {Dimensional} and {Supersymmetric} {Extensions} of {Loop} {Quantum} {Gravity}},
year = {2013}
}
@misc{faucris.114587484,
abstract = {

},
author = {Lang, Thorsten and et al.},
author_hint = {Lang T, Thiemann T},
faupublication = {yes},
peerreviewed = {automatic},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Hawking} {Radiation}},
year = {2011}
}
@article{faucris.123959704,
abstract = {In this work we investigate the question under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of "no-go theorems" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider, play an important role in loop quantum gravity since they can be defined without recurse to a background geometry and they might also be of interest in the general context of quantization of non-Abelian gauge theories. © 2011 American Institute of Physics.},
author = {Sahlmann, Hanno},
doi = {10.1063/1.3525706},
faupublication = {no},
journal = {Journal of Mathematical Physics},
peerreviewed = {Yes},
title = {{When} do measures on the space of connections support the triad operators of loop quantum gravity?},
volume = {52},
year = {2011}
}
@article{faucris.123229744,
abstract = {In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poisson-commuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11D SUGRA and 4D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the Rarita-Schwinger field. This is non-trivial because SUSY typically requires the Rarita-Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature.},
author = {Bodendorfer, Norbert and Thiemann, Thomas and Thurn, Andreas},
doi = {10.1088/0264-9381/30/4/045006},
faupublication = {yes},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Towards} loop quantum supergravity ({LQSG}): {I}. {Rarita}-{Schwinger} sector},
volume = {30},
year = {2013}
}
@article{faucris.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.109458404,
abstract = {We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction is the inclusion of new proposals for coupling matter to gravity that can be used to deparametrize the theory, thus making its dynamics more tractable. The classical and quantum aspects of these new proposals are explained alongside the standard quantization of vacuum general relativity in loop quantum gravity.},
author = {Giesel, Kristina and Sahlmann, Hanno},
faupublication = {yes},
journal = {PoS - Proceedings of Science},
pages = {55},
peerreviewed = {Yes},
title = {{From} {Classical} {To} {Quantum} {Gravity}: {Introduction} to {Loop} {Quantum} {Gravity}},
volume = {C11-02-28},
year = {2011}
}
@article{faucris.110423104,
abstract = {The quantum symmetry algebra corresponding to the generators of the little group faithfully represents the classical algebra.},
author = {Thiemann, Thomas},
faupublication = {no},
journal = {Classical and Quantum Gravity},
pages = {1463-1485},
peerreviewed = {Yes},
title = {{Quantum} spin dynamics ({QSD}): {VI}. {Quantum} {Poincare} algebra and a quantum positivity of energy theorem for canonical quantum gravity},
volume = {15},
year = {1998}
}
@masterthesis{faucris.111491864,
author = {Böhm, Benedikt and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{The} {Physical} {Hamiltonian} of the {Gowdy} {Model} in {Algebraic} {Quantum} {Gravity}},
year = {2015}
}
@misc{faucris.122499124,
author = {Sahlmann, Hanno and Seeger, Robert},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Geometric} properties of the {Livine}-{Speziale} coherent intertwiner},
year = {2015}
}
@masterthesis{faucris.111500004,
author = {Lang, Thorsten and Thiemann, Thomas},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Peakedness} properties of {SU}(3) heat kernel coherent states},
year = {2015}
}
@misc{faucris.118832824,
author = {Lohberger, Johannes and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Doubly} special relativity},
year = {2014}
}
@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.110401104,
abstract = {We investigate a certain distributional extension of the group of spatial diffeomorphisms in loop quantum gravity. This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category theory. These automorphisms have much larger orbits than piecewise analytic diffeomorphisms. In particular, we will show that graphs with the same combinatorics but different generalized knotting classes can be mapped into each other. We describe the automorphism-invariant Hilbert space and comment on how a combinatorial formulation of LQG might arise.},
author = {Bahr, Benjamin and Thiemann, Thomas},
doi = {10.1088/0264-9381/26/23/235022},
faupublication = {no},
journal = {Classical and Quantum Gravity},
peerreviewed = {Yes},
title = {{Automorphisms} in loop quantum gravity},
volume = {26},
year = {2009}
}
@masterthesis{faucris.200383145,
abstract = {The objective of this Master’s thesis is to consider the well-known framework of Weyl algebras and

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

quantum theory, to the theory of loop quantum gravity.

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

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

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

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

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

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

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

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

quantum gravity with the Fock space of a scalar field.

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

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

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

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

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

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

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

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.123219624, abstract = {We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four space-time dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state-independent factor. (C) 1998 American Institute of Physics.}, author = {Thiemann, Thomas}, faupublication = {no}, journal = {Journal of Mathematical Physics}, pages = {3347-3371}, peerreviewed = {Yes}, title = {{Closed} formula for the matrix elements of the volume operator in canonical quantum gravity}, volume = {39}, year = {1998} } @article{faucris.109461924, abstract = {In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity (AQG), was introduced. In the framework of AQG, existing semiclassical tools can be applied to operators that encode the dynamics of AQG such as the master constraint operator. In this paper, we will analyse the semiclassical limit of the (extended) algebraic master constraint operator and show that it reproduces the correct infinitesimal generators of general relativity. Therefore, the question of whether general relativity is included in the semiclassical sector of the theory, which is still an open problem in LQG, can be significantly improved in the framework of AQG. For the calculations, we will substitute SU(2) with U(1)(3). That this substitution is justified will be demonstrated in the third paper ( Giesel and Thiemann 2006 Semiclassical perturbation theory Preprint gr-qc/0607101) of this series.}, author = {Giesel, Kristina and Thiemann, Thomas}, doi = {10.1088/0264-9381/24/10/004}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {2499-2564}, peerreviewed = {Yes}, title = {{Algebraic} quantum gravity ({AQG}): {II}. {Semiclassical} analysis}, volume = {24}, year = {2007} }