arXiv subjects

Klaus Liegener

Publications and source records attributed to Klaus Liegener.

31 records · Page 2Linked to original sources

arXiv2019

Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of LQG in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and graph-preserving Hamiltonian is central, result in the formulation of a set of no-go statements, severely limiting the possibility of recovering a physically consistent effective dynamics this way.

gr-qc↗

arXiv2019

New Loop Quantum Cosmology Modifications from Gauge-covariant Fluxes

Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions build out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann in [1], we show that the physics of loop quantum cosmology is affected in a non-trivial way. The bounce turns out to be generically asymmetric with a rescaling of the Newton's constant in the pre-bounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched, resulting in an effective non-minimal coupling. These effects are shown to be common to different choices of regularization parameters.

gr-qc↗

arXiv2019

Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: $μ_0$ and $\bar μ$ in presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist also for Thiemann-regularized dynamics. The $μ_0$-scheme is found to be unviable as in standard loop quantum cosmology when a positive cosmological constant is included. Our investigation brings out a surprising result that the nature of emergent matter in the pre-bounce regime is determined by the choice of regulator in the Thiemann regularization of the scalar constraint whether or not one uses gauge-covaraint fluxes. Unlike $\bar μ$-scheme where the emergent matter is a cosmological constant, the emergent matter in $μ_0$-scheme behaves as a string gas.

gr-qc↗

arXiv2019

Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties

This is the third paper in a series of four in which a renormalisation flow is introduced which acts directly on the Osterwalder-Schrader data (OS data) without recourse to a path integral. Here the OS data consist of a Hilbert space, a cyclic vacuum vector therein and a Hamiltonian annihilating the vacuum which can be obtained from an OS measure, that is a measure respecting (a subset of) the OS axioms. In the previous paper we successfully tested our proposal for the two-dimensional massive Klein-Gordon model, that is, we could confirm that our framework finds the correct fixed point starting from a natural initial naive discretisation of the finite resolution Hamiltonians, in particular the underlying Laplacian on a lattice, and a natural coarse graining map that drives the renormalisation flow. However, several questions remained unanswered. How generic can the initial discretisation and the coarse graining map be in order that the fixed point is not changed or is at least not lost, in other words, how universal is the fixed point structure? Is the fix point in fact stable, that is, is the fixed point actually a limit of the renormalisation sequence? We will address these questions in the present paper.

gr-qc↗

arXiv2019

Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance

In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we introduce are explicitly computed for the D=2 case but transfer immediately to higher dimensions. In this article we define and verify a criterion that monitors, at finite resolution defined by a cubic lattice, whether the flow approaches a rotationally invariant fixed point.

gr-qc↗

arXiv2019

Hamiltonian Renormalisation II. Renormalisation Flow of 1+1 dimensional free scalar fields: Derivation

In the companion paper we motivated a renormalisation flow on Osterwalder-Schrader data (OS-data) consisting of 1. a Hilbert space, 2. a cyclic vacuum and 3. a Hamiltonian annihilating that vacuum. As the name suggests, the motivation was via the OS reconstruction theorem which allows to reconstruct the OS data from an OS measure satisfying (a subset of) the OS axioms, in particular reflection positivity. The guiding principle was to map the usual Wilsonian path integral renormalisation flow onto a flow of the corresponding OS data. We showed that this induced flow on the OS data has an unwanted feature which disqualifies the associated coarse grained Hamiltonians from being the projections of a continuum Hamiltonian onto vectors in the coarse grained Hilbert space. This motivated the definition of a direct Hamiltonian renormalisation flow which follows the guiding principle but does not suffer from the afore mentioned caveat. In order to test our proposal, we apply it to the only known completely solvable model, namely the case of free scalar quantum fields. In this paper we focus on the Klein Gordon field in two spacetime dimensions and illustrate the difference between the path integral induced and direct Hamiltonian flow. Generalisations to more general models in higher dimensions will be discussed in our companion papers.

gr-qc↗

arXiv2019

Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction

A possible avenue towards a non-perturbative Quantum Field Theory (QFT) on Minkowski space is the constructive approach which employs the Euclidian path integral formulation, in the presence of both ultraviolet (UV) and infrared (IR) regulators, as starting point. The UV regulator is to be taken away by renormalisation group techniques which in case of success leads to a measure on the space of generalised Euclidian fields in finite volume. The IR regulator corresponds to the thermodynamic limit of the system in the statistical physics sense. If the resulting measure obeys the Osterwalder-Schrader axioms, the actual QFT on Minkowski space is then obtained by Osterwalder-Schrader reconstruction. In this work we study the question whether it is possible to reformulate the renormalisation group non-perturbatively directly at the operator (Hamiltonian) level. Hamiltonian renormalisation would be the natural route to follow if one had easier access to an interacting Hamiltonian operator rather than to a path integral, at least in the presence of UV and/or IR cut-off, which is generically the case in complicated gauge theories such as General Relativity. Our guiding principle for the definition of the direct Hamiltonian renormalisation group is that it results in the same continuum theory as the covariant (path integral) renormalisation group. In order to achieve this, we invert the Osterwalder-Schrader reconstruction, which may be called Osterwalder-Schrader construction of a Wiener measure from the underlying Hamiltonian theory. The resulting correspondence between reflection positive measures and Osterwalder-Schrader data consisting of a Hilbert space, a Hamiltonian and a ground state vector allows us to monitor the effect of the renormalisation flow of measures in terms of their Osterwalder-Schrader data which motivates a natural direct Hamiltonian renormalisation scheme.

gr-qc↗

arXiv2019

Emergent de Sitter epoch of the Loop Quantum Cosmos: a detailed analysis

We present a detailed analysis of a quantum model for Loop Quantum Cosmology based on strict application of the Thiemann regularization algorithm for the Hamiltonian in Loop Quantum Gravity, extending the results presented previously in our brief report. This construction leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a spatially flat expanding Universe. Moreover, we present an effective Hamiltonian describing the quantum evolution to high accuracy and for which the dynamics can be solved analytically.

gr-qc↗

arXiv2018

Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics

The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes. We apply the same idea of its derivation in LQC to the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson-Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian.

gr-qc↗

arXiv2018

Emergent de Sitter epoch of the quantum Cosmos

The quantum nature of the Big Bang is reexamined in the framework of Loop Quantum Cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a flat expanding Universe.

gr-qc↗

arXiv2017

Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics

This is the first paper of a series dedicated to LQG coherent states and cosmology. The concept is based on the effective dynamics program of Loop Quantum Cosmology, where the classical dynamics generated by the expectation value of the Hamiltonian on semiclassical states is found to be in agreement with the quantum evolution of such states. We ask the question of whether this expectation value agrees with the one obtained in the full theory. The answer is in the negative. This series of papers is dedicated to detailing the computations that lead to that surprising result. In the current paper, we construct the family of coherent states in LQG which represent flat ($k=0$) Robertson-Walker spacetimes, and present the tools needed to compute expectation values of polynomial operators in holonomy and flux on such states. These tools will be applied to the LQG Hamiltonian operator (in Thiemann regularization) in the second paper of the series. The third paper will present an extension to $k\neq0$ cosmologies and a comparison with alternative regularizations of the Hamiltonian.

gr-qc↗

arXiv2016

Towards the fundamental spectrum of the Quantum Yang-Mills Theory

In this work we focus on the quantum Einstein-Yang-Mills sector quantised by the methods of Loop Quantum Gravity (LQG). We point out the improved UV behaviour of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact to the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relation of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.

gr-qc↗

arXiv2013

Matrix Elements of Lorentzian Hamiltonian Constraint in LQG

The Hamiltonian constraint is the key element of the canonical formulation of LQG coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires an heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations.

gr-qc↗