}, author = {Frembs, Markus and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{The} holonomy-flux algebra in low dimensions}, year = {2013} } @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.107352124, abstract = {We provide a precise definition and analysis of quantum causal histories (QCHs). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. We show that this local description of evolution is sufficient and that unitary evolution can be recovered wherever it should actually be expected. This formalism may describe a quantum cosmology without an assumption of global hyperbolicity; it is thus more general than the Wheeler-De Witt approach. The structure of a QCH is also closely related to quantum information theory and algebraic quantum field theory on a causal set.}, author = {Hawkins, Eli and Markopoulou, Fotini and Sahlmann, Hanno}, doi = {10.1088/0264-9381/20/16/320}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {3839-3854}, peerreviewed = {Yes}, title = {{Evolution} in quantum causal histories}, volume = {20}, year = {2003} } @article{faucris.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.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.115365844, abstract = {We follow arguments of Verlinde (2010 arXiv:1001.0785 [hep-th]) and Klinkhamer (2010 arXiv:1006.2094 [hep-th]), and construct two models of the microscopic theory of a holographic screen that allow for the thermodynamical derivation of Newton's law, with Newton's constant expressed in terms of a minimal length scale l contained in the area spectrum of the microscopic theory. One of the models is loosely related to the quantum structure of surfaces and isolated horizons in loop quantum gravity. Our investigation shows that the conclusions reached by Klinkhamer regarding the new length scale l seem to be generic in all their qualitative aspects. © 2011 IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/0264-9381/28/1/015006}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Newton}'s constant from a minimal length: {Additional} models}, volume = {28}, year = {2011} } @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.

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.

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.118093844,
abstract = {This thesis is devoted to the study of the quantum theory of charged black holes in the context of loop quantum gravity, extending the model of the quantum black hole as considered so far in the literature. We therefore consider Maxwell theory coupled to gravity de ned on a spacetime manifold with internal boundary described by an isolated horizon, construct the Hamiltonian formulation of the classical system, quantize the corresponding symplectic phase space and nally go over to the computation of the black hole entropy. We consider the spherically symmetric case in the U(1) framework as well as the distorted case following the SU(2) approach. The resulting picture depends signi cantly on the choices made for the quantization and the de nition of the state counting. We show that there is a choice such that the Bekenstein-Hawking relation holds. At the end, we use the theory in order to address the question whether there is a correspondence between the highly damped quasinormal modes and the area spectra of quantum charged black holes in the framework of loop quantum gravity. },
author = {Eder, Konstantin and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Quantum} theory of charged black hole horizons},
year = {2017}
}
@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.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.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.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.108871884,
abstract = {In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of ground- or KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-pnt function is of Hadamard form). The fields can be of bosonic or fermionic character. We also give an abstract version of this result by showing that passive states of a topological *-dynamical system have an asymptotic pair correlation spectrum of a specific type.},
author = {Sahlmann, Hanno and Verch, Rainer},
faupublication = {no},
journal = {Communications in Mathematical Physics},
pages = {705-731},
peerreviewed = {Yes},
title = {{Passivity} and microlocal spectrum condition},
url = {https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=0034343139&origin=inward},
volume = {214},
year = {2000}
}
@misc{faucris.122499124,
author = {Sahlmann, Hanno and Seeger, Robert},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Geometric} properties of the {Livine}-{Speziale} coherent intertwiner},
year = {2015}
}
@article{faucris.115364084,
abstract = {Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a brief description of the main structures and results of quantum geometry, I review a new description of the quantized geometry in terms of polyhedra, new results on the volume operator, and a way to incorporate a classical background metric into the quantum description. Finally I describe a new type of exponentiated flux operator, and its application to Chern-Simons theory and black holes. © Published under licence by IOP Publishing Ltd.},
author = {Sahlmann, Hanno},
doi = {10.1088/1742-6596/360/1/012007},
faupublication = {no},
journal = {Journal of Physics : Conference Series},
peerreviewed = {No},
title = {{New} insights in quantum geometry},
volume = {360},
year = {2012}
}
@article{faucris.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}
}
@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}
}
@misc{faucris.111477124,
author = {Roelcke, Carmen and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Conical} space-time defects and their phenomenological consequences},
year = {2015}
}
@masterthesis{faucris.108049744,
abstract = {The dynamical laws of an evolving system determine how the system will look at later times, given some initial state the system started from. In quantum cosmology, one ap- plies this idea to the earliest moments of the universe, which requires one to have some idea about the intial conditions at the beginning of time. One proposal describing these initial conditions in the context of canonical quantum gravity is due to Hartle and Hawk- ing. Their proposal entails a preferred initial state for the universe which is based on a Euclidean path integral over all compact positive definite four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the constraint equations of general relativity in ADM variables in a formal sense.

},
author = {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}
}
@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.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.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}
}
@incollection{faucris.116261244,
abstract = {We introduce a notion of a weak Poisson structure on a manifold *M* modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra A⊆C∞(M)" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="0">A⊆C∞(M) which has to satisfy a non-degeneracy condition (the differentials of elements of A" id="MathJax-Element-2-Frame" role="presentation" style="position: relative;" tabindex="0">A separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form *κ* on a Lie algebra g" id="MathJax-Element-3-Frame" role="presentation" style="position: relative;" tabindex="0">g and a *κ*-skew-symmetric derivation *D* a weak affine Poisson structure on g" id="MathJax-Element-4-Frame" role="presentation" style="position: relative;" tabindex="0">g itself. This leads naturally to a concept of a Hamiltonian *G*-action on a weak Poisson manifold with a g" id="MathJax-Element-5-Frame" role="presentation" style="position: relative;" tabindex="0">g

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

}, author = {Neeb, Karl-Hermann and Thiemann, Thomas and Sahlmann, Hanno}, booktitle = {Springer Proceedings in Mathematics & Statistics}, editor = {V. Dobrev}, faupublication = {yes}, isbn = {978-4-431-55284-0}, pages = {105-136}, peerreviewed = {unknown}, publisher = {Springer Japan}, title = {{Weak} {Poisson} structures on infinite dimensional manifolds and hamiltonian actions}, url = {https://arxiv.org/abs/1402.6818}, volume = {111}, year = {2015} } @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.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.120516264, abstract = {We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint. © 2008 IOP Publishing Ltd.}, author = {Sahlmann, Hanno and Fewster, Christopher}, doi = {10.1088/0264-9381/25/22/225015}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Phase} space quantization and loop quantum cosmology: {A} {Wigner} function for the {Bohr}-compactified real line}, volume = {25}, year = {2008} } @article{faucris.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} } @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.115355504, abstract = {As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism-invariant states for a scalar field. We give a very explicit formula for the scalar product on this space and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism-invariant quantities on that space and discuss in detail the ordering issues involved. On a technical level these issues bear some similarity to those encountered in full loop quantum gravity. © 2007 IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/0264-9381/24/18/003}, faupublication = {no}, journal = {Classical and Quantum Gravity}, pages = {4601-4615}, peerreviewed = {Yes}, title = {{Exploring} the diffeomorphism-invariant {Hilbert} space of a scalar field}, volume = {24}, year = {2007} } @article{faucris.123221164, abstract = {We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far. (C) 2001 Elsevier Science B.V. All rights reserved.}, author = {Sahlmann, Hanno and Thiemann, Thomas and Winkler, Oliver}, faupublication = {no}, journal = {Nuclear Physics B}, pages = {401-440}, peerreviewed = {Yes}, title = {{Coherent} states for canonical quantum general relativity and the infinite tensor product extension}, volume = {606}, year = {2001} } @masterthesis{faucris.119253244, author = {Zilker, Thomas and Giesel, Kristina}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Manifestly} {Gauge} {Invariant} {Cosmological} {Perturbation} {Theory}}, year = {2013} } @article{faucris.115339224, abstract = {In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling back, the quantized bulk degrees of freedom. This is not yet fully realized in the-otherwise very successful-quantization of isolated horizons in loop quantum gravity. In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. There is no need to quantize them separately. We present evidence that for a horizon of sphere topology, the resulting horizon theory is remarkably similar to what has been found before. © 2011 American Physical Society.}, author = {Sahlmann, Hanno}, doi = {10.1103/PhysRevD.84.044049}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, keywords = {black holes; quantum gravity; horizons; loop quantum gravity}, peerreviewed = {Yes}, title = {{Black} hole horizons from within loop quantum gravity}, volume = {84}, year = {2011} } @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} } @misc{faucris.120250284, author = {Sahlmann, Hanno and Wolz, Florian}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Geometric} meaning of the {Penrose} metric}, year = {2014} } @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} } @misc{faucris.120355224, author = {Sahlmann, Hanno and Beier, Udo}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Defects} as a model of spacetime foam - {Spinor} and vector structures on the defect}, year = {2015} } @article{faucris.115368044, abstract = {In loop quantum gravity, matter fields can have support only on the 'polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states cannot refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background-independent operator algebras and Hilbert spaces. Second, to make contact with low-energy physics, one has to relate this 'polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.}, author = {Sahlmann, Hanno and Ashtekar, Abhay and Lewandowski, Jerzy}, doi = {10.1088/0264-9381/20/1/103}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{Polymer} and {Fock} representations for a scalar field}, volume = {20}, year = {2003} } @masterthesis{faucris.121097064, abstract = {String theory is one of the candidates for a theory that not only describes the nature of gravity at microscopic scales but also unites all fundamental forces into one common framework. This is possible by the simple assumption that all matter is given by small one-dimensional objects – strings – that may be open or closed.

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

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

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

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

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

}, author = {Wolz, Florian and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{On} spatially diffeomorphism invariant quantizations of the bosonic string}, year = {2015} } @misc{faucris.109674664, author = {Wasserka, Tony and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Four}-valent vertex and the {Penrose} metric}, year = {2014} } @article{faucris.123504524, abstract = {In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family of gravitational scalar constraints. They preserve the Hilbert space for every choice of lapse function. Thus adjointness and commutator properties of the constraint can be investigated in a straightforward manner. We show how the space of solutions of the symmetrized constraint can be defined by spectral decomposition, and the Hilbert space of physical states by subsequently fully implementing the diffeomorphism constraint. The relationship of the solutions to those resulting from a proposal for a symmetric constraint operator by Thiemann remains to be elucidated.}, author = {Sahlmann, Hanno and Lewandowski, Jerzy}, doi = {10.1103/PhysRevD.91.044022}, faupublication = {yes}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, peerreviewed = {unknown}, title = {{Symmetric} scalar constraint for loop quantum gravity}, volume = {91}, year = {2015} }