% Encoding: UTF-8 @COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/} @COMMENT{For any questions please write to cris-support@fau.de} @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.201147872, abstract = {We study the asymptotic behaviour of the vertex amplitude for the EPRL spin foam model extended to include timelike tetrahedra. We analyze both, tetrahedra of signature --- (standard EPRL), as well as of signature +-- (Hnybida-Conrady extension), in a unified fashion. However, we assume all faces to be of signature --. We find that the critical points of the extended model are described again by 4-simplices and the phase of the amplitude is equal to the Regge action. Interestingly, in addition to the Lorentzian and Euclidean sectors there appear also split signature 4-simplices.}, author = {Sahlmann, Hanno and Kaminski, Wojciech and Kisielowski, Marcin}, doi = {10.1088/1361-6382/aac6a4}, faupublication = {yes}, journal = {Classical and Quantum Gravity}, keywords = {quantum gravity;spin foam;EPRL model;stationary phase analysis;large spin limit}, peerreviewed = {Yes}, title = {{Asymptotic} analysis of the {EPRL} model with timelike tetrahedra}, volume = {35}, year = {2018} } @article{faucris.115339224, abstract = {In general relativity, the fields on a black hole horizon are obtained from those in the bulk by pullback and restriction. Similarly, in quantum gravity, the quantized horizon degrees of freedom should result from restricting, or pulling back, the quantized bulk degrees of freedom. This is not yet fully realized in the-otherwise very successful-quantization of isolated horizons in loop quantum gravity. In this work we outline a setting in which the quantum horizon degrees of freedom are simply components of the quantized bulk degrees of freedom. There is no need to quantize them separately. We present evidence that for a horizon of sphere topology, the resulting horizon theory is remarkably similar to what has been found before. © 2011 American Physical Society.}, author = {Sahlmann, Hanno}, doi = {10.1103/PhysRevD.84.044049}, faupublication = {no}, journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology}, keywords = {black holes; quantum gravity; horizons; loop quantum gravity}, peerreviewed = {Yes}, title = {{Black} hole horizons from within loop quantum gravity}, volume = {84}, year = {2011} } @article{faucris.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.115353084, abstract = {We consider a novel derivation of the expectation values of holonomies in Chern-Simons theory, based on Stokes' Theorem and the functional properties of the Chern-Simons action. It involves replacing the connection by certain functional derivatives under the path integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity. © 2011 Elsevier B.V.}, author = {Sahlmann, Hanno and Thiemann, Thomas}, doi = {10.1016/j.geomphys.2011.02.013}, faupublication = {yes}, journal = {Journal of Geometry and Physics}, keywords = {Chern-Simons theory; Duflo map; Loop quantum gravity}, pages = {1104-1121}, peerreviewed = {Yes}, title = {{Chern}-{Simons} theory, {Stokes}' theorem, and the {Duflo} map}, volume = {61}, year = {2011} } @article{faucris.123221164, abstract = {We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far. (C) 2001 Elsevier Science B.V. All rights reserved.}, author = {Sahlmann, Hanno and Thiemann, Thomas and Winkler, Oliver}, faupublication = {no}, journal = {Nuclear Physics B}, pages = {401-440}, peerreviewed = {Yes}, title = {{Coherent} states for canonical quantum general relativity and the infinite tensor product extension}, volume = {606}, year = {2001} } @article{faucris.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} } @misc{faucris.111477124, author = {Roelcke, Carmen and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Conical} space-time defects and their phenomenological consequences}, year = {2015} } @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} } @misc{faucris.118832824, author = {Lohberger, Johannes and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Doubly} special relativity}, year = {2014} } @masterthesis{faucris.200464729, abstract = {
The inflationary epoch at the beginning of the universe is commonly described within the frame- work of (linear) cosmological perturbation theory. The corresponding equation of motion for the gauge-invariant perturbations is the Mukhanov-Sasaki equation, which resembles a time-dependent harmonic oscillator. At first we will consider a mechanical analogue of the Mukhanov-Sasaki equa- tion and use the known Lewis-Riesenfeld invariant and the extended phase space formalism in- troduced in previous works in order to analyse the system. These techniques allow to construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one. The generators of this symplectic map can in turn be canonically quan- tised on the original part of the phase space, which is the constraint hypersurface of the extended theory, connecting to recent publications. Our further analysis leads us to a closed form of the time-evolution operator for the single-mode Mukhanov-Sasaki Hamiltonian, that is to the associ- ated Dyson series. We will analyse the characteristic properties of this time-evolution operator and discuss whether it can be extended to the full Fock space. Finally we give an outlook towards possible applications of these techniques to inflationary quantum cosmology.
In the present thesis, we give a general definition of a Gaussian measure over (Abelian) connections, and study their properties. In particular, we define the holonomy-flux Weyl algebra for U(1). Then we investigate the absolute continuity of Gaussian measures with respect to representations of the Weyl algebra and the unitary implementation of gauge transformations. This shows that for a large subclass, the lengthlike Gaussian measures, there are no representations in which the exponentiated fluxes are implemented unitarily. We also determine some structural properties of Gaussian measures which are invariant under Euclidean transformations of the base manifold. As a side result, we discuss how new methods from analysis can be employed to show, how results obtained with well known algebraic techniques can be reproduced and strengthened using recent results on the convergence of Fourier series.
}, 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.120250284, author = {Sahlmann, Hanno and Wolz, Florian}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Geometric} meaning of the {Penrose} metric}, year = {2014} } @misc{faucris.122499124, author = {Sahlmann, Hanno and Seeger, Robert and Seeger, Robert}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Geometric} properties of the {Livine}-{Speziale} coherent intertwiner}, year = {2015} } @misc{faucris.123776664, author = {Stritzelberger, Nadine and Sahlmann, Hanno}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Geometrische} {Eigenschaften} der {Verschränkungsentropie} in der {Loop}-{Quantengravitation}}, year = {2014} } @article{faucris.256248612, author = {Sahlmann, Hanno and Grüber, David and Zilker, Thomas}, doi = {10.1103/PhysRevD.98.066009}, faupublication = {yes}, journal = {Physical Review D}, peerreviewed = {Yes}, title = {{Geometry} and entanglement entropy of surfaces in loop quantum gravity}, volume = {98}, year = {2018} } @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} } @incollection{faucris.256248882, author = {Sahlmann, Hanno}, booktitle = {Springer Handbook of Spacetime}, doi = {10.1007/978-3-642-41992-8{\_}37}, editor = {Ashtekar, Abhay; Petkov, Vesselin}, faupublication = {yes}, isbn = {9783642419928}, pages = {759-782}, peerreviewed = {Yes}, publisher = {Springer Berlin Heidelberg}, series = {Springer Handbooks}, title = {{Gravity}, geometry, and the quantum}, year = {2014} } @article{faucris.261661710, abstract = {In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for $\mathcal{N}=1$ and $\mathcal{N}=2$ pure AdS supergravity in $D=4$ for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the $\mathcal{N}=2$ case, it follows that this amounts to the introduction of a $\theta$-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the $\theta$-ambiguity of gauge theory.
We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with $\mathrm{OSp}(\mathcal{N}|2)$ gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D'Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravit}, author = {Eder, Konstantin and Sahlmann, Hanno}, doi = {10.1007/JHEP07(2021)071}, faupublication = {yes}, journal = {Journal of High Energy Physics}, keywords = {Supergravity Models, AdS-CFT Correspondence, Chern-Simons Theories}, peerreviewed = {Yes}, title = {{Holst}-{MacDowell}-{Mansouri} action for (extended) supergravity with boundaries and super {Chern}-{Simons} theory}, volume = {2021}, year = {2021} } @article{faucris.118959324, abstract = {We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and an su(2)-valued one-form, obeying certain constraints. The horizon symplectic structure is precisely the one of 3d gravity in a first order formulation. We quantize the horizon degrees of freedom in the framework of loop quantum gravity, with methods recently developed for 3d gravity with non-vanishing cosmological constant. Bulk excitations ending on the horizon act very similarly to particles in 3d gravity. The Bekenstein-Hawking law is recovered in the limit of imaginary Barbero-Immirzi parameter. Alternative methods of quantization are also discussed.}, author = {Sahlmann, Hanno and Pranzetti, Daniele}, doi = {10.1016/j.physletb.2015.04.070}, faupublication = {yes}, journal = {Physics Letters B}, pages = {209-216}, peerreviewed = {Yes}, title = {{Horizon} entropy with loop quantum gravity methods}, volume = {746}, year = {2015} } @article{faucris.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.259299440, abstract = {Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity. There is a general understanding of how to formulate scalar fields, spin 12 fields, and gauge fields in the framework of loop quantum gravity. The goal of the present work is to investigate kinematical aspects of this coupling. We will study implications of the Gauß and diffeomorphism constraints for the quantum theory: We define and study a less ambiguous variant of the Baez-Krasnov path observables, and we investigate symmetry properties of spin network states imposed by diffeomorphism group averaging. We will do this in a setting which allows for matter excitations of spin 12 and higher. In the case of spin 12, we will also discuss extensions of it by introducing an electromagnetic field and antiparticles. We finally discuss how far the picture with matter excitations of higher spin can be obtained from classical actions for higher spin fields.}, author = {Mansuroglu, Refik and Sahlmann, Hanno}, doi = {10.1103/PhysRevD.103.106010}, faupublication = {yes}, journal = {Physical Review D}, note = {CRIS-Team Scopus Importer:2021-05-28}, peerreviewed = {Yes}, title = {{Kinematics} of arbitrary spin matter fields in loop quantum gravity}, volume = {103}, year = {2021} } @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.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.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} } @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.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.251039899, abstract = {In this paper, the classical and quantum theory of N=1 supergravity in four spacetime dimensions will be studied in the framework of loop quantum gravity. We discuss the canonical analysis of the supergravity Holst action as first introduced by Tsuda. In this way, we also derive a compact expression of the supersymmetry constraint, which plays a crucial role in canonical supergravity theories, akin to the role of the Hamiltonian constraint in nonsupersymmetric generally covariant theories. The resulting theory is then quantized using loop quantum gravity methods. In particular, we propose and discuss a quantization of the supersymmetry constraint and derive explicit expressions of the action of the resulting operator. This is important as it is the first step on the way to analyzing the Dirac algebra generated by supersymmetry and Hamiltonian constraint in the quantum theory and for finding physical states. We also discuss some qualitative properties of such solutions of the SUSY constraint. }, author = {Eder, Konstantin and Sahlmann, Hanno}, doi = {10.1103/PhysRevD.103.046010}, faupublication = {yes}, journal = {Physical Review D}, note = {CRIS-Team Scopus Importer:2021-03-05}, peerreviewed = {Yes}, title = {{N}=1 {Supergravity} with loop quantum gravity methods and quantization of the {SUSY} constraint}, volume = {103}, year = {2021} } @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.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} } @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.289294162, abstract = {Perfect tensors describe highly entangled quantum states that have attracted particular attention in the fields of quantum information theory and quantum gravity. In loop quantum gravity, the natural question arises whether SU(2) invariant tensors, which are fundamental ingredients of the basis states of spacetime, can also be perfect. In this work, we present a number of general constraints for the layout of such invariant perfect tensors (IPTs) and further describe a systematic and constructive approach to check the existence of an IPT of given valence. We apply our algorithm to show that no qubit encoding of valence 6 can be described by an IPT and close a gap to prove a no-go theorem for invariant perfect qubit encodings. We also provide two alternative proofs for the non-existence of 4-valent qubit IPTs which has been shown in [1, 2].}, author = {Mansuroglu, Refik and Sahlmann, Hanno}, doi = {10.1007/JHEP02(2023)062}, faupublication = {yes}, journal = {Journal of High Energy Physics}, keywords = {Gauge-Gravity Correspondence; Holography and Condensed Matter Physics (AdS/CMT); Models of Quantum Gravity}, note = {CRIS-Team Scopus Importer:2023-02-17}, peerreviewed = {Yes}, title = {{No} invariant perfect qubit codes}, volume = {2023}, year = {2023} } @article{faucris.120515604, abstract = {In a remarkable paper (Koslowski T A 2007 arXiv:0709.3465[gr-qc]), Koslowski introduced kinematical representations for loop quantum gravity in which a non-degenerate spatial background metric is present. He also considered their properties and showed that Gauß and diffeomorphism constraints can be implemented. With this paper, we streamline and extend his treatment. In particular, we show that the standard regularization of the geometric operators leads to well-defined operators in the new representations, and we work out their properties fully. We also give details on the implementation of the constraints. All of this is done in such a way as to show that the standard representation is a particular (and in some ways exceptional) case of the more general constructions. This does not mean that these new representations are as fundamental as the standard one. Rather, we believe they might be useful to find some form of effective theory of loop quantum gravity on large scales. © 2010 IOP Publishing Ltd.}, author = {Sahlmann, Hanno}, doi = {10.1088/0264-9381/27/22/225007}, faupublication = {no}, journal = {Classical and Quantum Gravity}, peerreviewed = {Yes}, title = {{On} loop quantum gravity kinematics with a non-degenerate spatial background}, volume = {27}, year = {2010} } @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} } @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.
Following the connection formulation, general relativity can be equivalently recast using the so-called Ashtekar-Barbero variables. The idea followed in this thesis is to mimic Hartle’s and Hawking’s procedure to construct an initial state in terms of these new variables. We observe that the wave function constructed this way does not satisfy the constraint equations of loop quantum gravity, even in a formal sense. We investigate this issue in the simple case of a relativistic particle. We finally suggest a modification of the proposal that does satisfy the constraints at least in a formal sense and start to consider its implications in quantum cosmology.
We finally show that in two dimensions and for the abelian case, holonomy-flux-algebras can be related to Weyl algebras in a simple way.
},
author = {Frembs, Markus and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
title = {{The} holonomy-flux algebra in low dimensions},
year = {2013}
}
@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.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.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}
}
@misc{faucris.259457368,
author = {Banarescu, Marvin and Kobler, Michael and Giesel, Kristina},
faupublication = {yes},
peerreviewed = {automatic},
title = {{The} {Spin}-{Boson} {Model} with a time-dependent {Oscillator} {Environment}},
year = {2021}
}
@article{faucris.277748935,
abstract = {Recently, many geometric aspects of N-extended anti–de Sitter supergravity in chiral variables have been encountered and clarified. In particular, if the theory is supposed to be invariant under supersymmetry transformations also on boundaries, the boundary term has to be the action of an OSp(N|2)C super Chern-Simons theory, and particular boundary conditions must be met. Based on this, we propose a way to calculate an entropy S for surfaces, presumably including black hole horizons, in the supersymmetric version of loop quantum gravity for the minimal case N=1. It proceeds in analogy to the nonsupersymmetric theory, by calculating dimensions of quantum state spaces of the super Chern-Simons theory with punctures, for a fixed quantum (super) area of the surface. We find S=a{\_}H/4 for large areas and determine the subleading correction. Because of the noncompactness of OSp(1|2)C and the corresponding difficulties with the Chern-Simons quantum theory, we use analytic continuation from the Verlinde formula for a compact real form, UOSp(1|2), in analogy to work by Noui et al. This also entails studying some properties of OSp(1|2){\_}C representations that we have not found elsewhere in the literature.
quasifree states in order to find out if it is possible to apply the general ideas, coming from algebraic
quantum theory, to the theory of loop quantum gravity.
Starting from the U(1) toy-model of the canonical commutation relation of the holonomy-flux
algebra, underlying loop quantum gravity, we construct a Weyl C*-algebra generated by so-called
Weyl elements that arise from combining holonomies and exponentiated electric fluxes, which are
the canonically conjugated variables of the theory. Quasifree states are a certain notion of Gaussian
states, directly emerging from Weyl algebras. Because it seems to be impossible to establish such
states on the algebra we found, we develop a different notion states that is only Gaussian in one of
the variables and hence is referred to as almost-quasifree states. For such a state, which is Gaussian
in the fluxes, we find a representation on a Hilbert space that combines the Hilbert space of loop
quantum gravity with the Fock space of a scalar field.
For the canonical commutation relation of the actual theory, which involves SU(2) Yang-Mills
holonomies and the corresponding fluxes, we try to generalize our results. It is possible to define
Weyl-like elements for holonomies along a single path and a set of exponentiated fluxes. We work
toward a notion of elements that take care of more distinct edges or even graphs. It is, however,
not clear if these also generate a C*-algebra. Without an underlying Weyl algebra we successfully
generalize the almost-quasifree representation, found for the toy-model, and analyze its properties
by re-deriving the area operator of loop quantum gravity in this new representation.
M modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra A⊆C∞(M)" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="0">A⊆C∞(M) which has to satisfy a non-degeneracy condition (the differentials of elements of A" id="MathJax-Element-2-Frame" role="presentation" style="position: relative;" tabindex="0">A separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form κ on a Lie algebra g" id="MathJax-Element-3-Frame" role="presentation" style="position: relative;" tabindex="0">g and a κ-skew-symmetric derivation D a weak affine Poisson structure on g" id="MathJax-Element-4-Frame" role="presentation" style="position: relative;" tabindex="0">g itself. This leads naturally to a concept of a Hamiltonian G-action on a weak Poisson manifold with a g" id="MathJax-Element-5-Frame" role="presentation" style="position: relative;" tabindex="0">g
-valued momentum map and hence to a generalization of quasi-hamiltonian group actions.
}, author = {Neeb, Karl-Hermann and Thiemann, Thomas and Sahlmann, Hanno}, booktitle = {Springer Proceedings in Mathematics & Statistics}, editor = {V. Dobrev}, faupublication = {yes}, isbn = {978-4-431-55284-0}, pages = {105-136}, peerreviewed = {unknown}, publisher = {Springer Japan}, title = {{Weak} {Poisson} structures on infinite dimensional manifolds and hamiltonian actions}, url = {https://arxiv.org/abs/1402.6818}, volume = {111}, year = {2015} } @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.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} }