arXiv subjects

Hanno Sahlmann

Publications and source records attributed to Hanno Sahlmann.

At least 37 records · Page 2Linked to original sources

arXiv2021

Fermion spins in loop quantum gravity

We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong entanglement between gravity and fermionic degrees of freedom. Interestingly we find that properties and spectra of the observables are nevertheless similar to their counterparts from quantum mechanics. However, there are also new effects. Due to the entanglement between gravity and fermionic degrees of freedom, alignment of quantum spins has consequences for quantized geometry. We sketch a particular effect of this kind that may in principle be observable.

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arXiv2021

Supersymmetric minisuperspace models in self-dual loop quantum cosmology

In this paper, we study a class of symmetry reduced models of $\mathcal{N}=1$ supergravity using self-dual variables. It is based on a particular Ansatz for the gravitino field as proposed by D'Eath et al. We show that the essential part of the constraint algebra in the classical theory closes. In particular, the (graded) Poisson bracket between the left and right supersymmetry constraint reproduces the Hamiltonian constraint. For the quantum theory, we apply techniques from the manifestly supersymmetric approach to loop quantum supergravity, which yields a graded analog of the holonomy-flux algebra and a natural state space. We implement the remaining constraints in the quantum theory. For a certain subclass of these models, we show explicitly that the (graded) commutator of the supersymmetry constraints exactly reproduces the classical Poisson relations. In particular, the trace of the commutator of left and right supersymmetry constraints reproduces the Hamilton constraint operator. Finally, we consider the dynamics of the theory and compare it to a quantization using standard variables and standard minisuperspace techniques.

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arXiv2020

$\mathcal{N}=1$ Supergravity with LQG methods and quantization of the SUSY constraint

In this paper, the classical and quantum theory of $\mathcal{N}=1$ 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 non-supersymmetric 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 of 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.

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arXiv2020

Towards Gaussian states for loop quantum gravity

An important challenge in loop quantum gravity is to find semiclassical states - states that are as close to classical as quantum theory allows. This is difficult because the states in the Hilbert space used in LQG are excitations over a vacuum in which geometry is highly degenerate. Additionally, fluctuations are distributed very unevenly between configuration and momentum variables. Coherent states that have been proposed to balance the uncertainties more evenly can, up to now, only do this for finitely many degrees of freedom. Our work is motivated by the desire to obtain Gaussian states that encompass all degrees of freedom. To obtain a toy-model we reformulate the U(1) holonomy-flux algebra in any dimension as a Weyl algebra, and discuss generalisations to SU(2). We then define and investigate a new class of states on these algebras which behave like quasifree states on the momentum variables.

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arXiv2019

Quantum surface holonomies for loop quantum gravity and their application to black hole horizons

In this work we define a new type of flux operators on the Hilbert space of loop quantum gravity. We use them to solve an equation of the form $F(A)=c\,Σ$ in loop quantum gravity. This equation, which relates the curvature of a connection $A$ with its canonical conjugate $Σ=*E$, plays an important role for spherically symmetric isolated horizons, and, more generally, for maximally symmetric geometries and for the Kodama state. If the equation holds, the new flux operators can be interpreted as a quantization of surface holonomies from higher gauge theory. Also, they represent a kind of quantum deformation of SU(2). We investigate their properties and discuss how they can be used to define states that satisfy the isolated horizon boundary condition in the quantum theory.

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arXiv2019

The hessian in spin foam models

We fill one of the remaining gaps in the asymptotic analysis of the vertex amplitudes of the Engle-Pereira-Rovelli-Livine (EPRL) spin foam models: We show that the hessian is nondegenerate for the stationary points that corresponds to geometric nondegenerate $4$ simplices. Our analysis covers the case when all faces are spacelike.

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arXiv2019

Asymptotic analysis of the EPRL model with timelike tetrahedra

We perform the stationary phase analysis of the vertex amplitude for the EPRL spin foam model extended to include timelike tetrahedra. We analyse 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 $--$. The stationary 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.

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arXiv2018

The geometry and entanglement entropy of surfaces in loop quantum gravity

In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature and mean curvature. By investigating their properties, we shed light on the nature of the geometry of surfaces in loop quantum gravity. We also investigate the entanglement entropy across surfaces in the case where spin network edges are running within the surface. We observe that, on a certain class of states, the entropy gradient across a surface is proportional to the mean curvature. In particular, the entanglement entropy is constant for small deformations of a minimal surface in this case.

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arXiv2018

Quantum theory of charged isolated horizons

We describe the quantum theory of isolated horizons with electromagnetic or non-Abelian gauge charges in a setting in which both gauge and gravitational field are quantized. We consider the distorted case, and its spherically symmetric limit. We show that the gravitational horizon degrees of freedom 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 degrees of freedom into the state counting. We show that one can expect (potentially divergent) contributions proportional to the area, as well as logarithmic correction proportional to the horizon charge. This is qualitatively similar to results on matter contributions obtained with other methods in the literature.

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arXiv2017

Extensions of the Duflo map and Chern-Simons expectation values

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.

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arXiv2016

Towards a Hartle-Hawking state for loop quantum gravity

The Hartle-Hawking state is a proposal for a preferred initial state for quantum gravity, based on a path integral over all compact Euclidean four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the (Lorentzian) Hamiltonian constraint of general relativity in ADM variables in a formal sense. In this article we mimic this procedure of constructing an initial state in terms of Ashtekar-Barbero variables, and observe that the wave function thus constructed does not satisfy the Lorentzian Hamiltonian constraint even in a formal sense. We also investigate this issue for the relativistic particle. We finally suggest a modification of the proposal that does satisfy the constraint at least in a formal sense and start to consider its implications in quantum cosmology. We find that for certain variables, and in the saddle point approximation, the state is very similar to the Ashtekar-Lewandowski state of loop quantum gravity.

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arXiv2015

Loop quantum gravity coupled to a scalar field

We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field. Several new results for loop quantum gravity are obtained: (i) a Hilbert space for the gravity-matter system and a non-standard 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 constraint do not vanish, but seem to reproduce a part of the Dirac algebra. 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 bears a strong resemblance to the BF vacuum of Dittrich and Geiller.

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arXiv2015

Horizon entropy with loop quantum gravity methods

We show that the spherically symmetric isolated horizon can be described in terms of an SU(2) connection and a 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 similar 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.

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arXiv2015

A symmetric scalar constraint for loop quantum gravity

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.

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arXiv2013

No-boundary measure and preference for large e-foldings in multi-field inflation

The no-boundary wave function of quantum gravity usually assigns only very small probability to long periods of inflation. This was a reason to doubt about the no-boundary wave function 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 wave function can give higher probability for sufficient inflation, but the number of fields involved has to be very high.

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arXiv2013

From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity

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.

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arXiv2012

The no-boundary measure in string theory: Applications to moduli stabilization, flux compactification, and cosmic landscape

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 wave function 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 wave function 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 for de Sitter.

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arXiv2012

Loop Quantum Gravity Vacuum with Nondegenerate Geometry

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.

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