On Generalised Statistical Equilibrium and Discrete Quantum Gravity (Springer Theses)

✍ Scribed by Isha Kotecha

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 194
• Category: Library

✦ Synopsis

Absolute concepts of time and energy are integral to standard thermal physics, but background independent systems are devoid of them. This thesis explores the foundational question of generalising equilibrium statistical mechanics to background independent systems, and applies the resulting formulation to non-perturbative discrete quantum gravity. It offers a discussion of the rich interface of thermal physics and quantum gravity in this context, providing a broad contextualisation of such topics. This work details how standard tools from many-body physics can be generalised to discrete quantum gravity labelled with graph-based, or dual polyhedral, quanta that are common to various approaches like tensorial group field theory, loop quantum gravity, dynamical triangulations and lattice quantum gravity. It provides a systematic investigation, both conceptual and technical, of quantum gravitational Gibbs states, thermofield double vacuum states, and their application in condensate cosmology to probe questions of Big Bang singularity resolution and geometric inflation.

✦ Table of Contents

Supervisor’s Foreword
Abstract
Acknowledgements
Contents
1 Introduction
1.1 Thermal Physics, Gravity and Quantum Theory
1.2 Why Search for Quantum Gravity
1.3 Outline of the Thesis
References
2 Generalised Statistical Equilibrium
2.1 Rethinking Time in Mechanics
2.1.1 Preliminaries: Presymplectic Mechanics
2.1.2 Deparametrization
2.2 Generalised Gibbs Equilibrium
2.2.1 Characterising Gibbs States
2.2.2 Past Proposals
2.2.3 Thermodynamical Characterisation
2.2.4 Modular Flows and Stationarity
2.2.5 Remarks
2.3 Generalised Thermodynamics
2.3.1 Thermodynamic Potentials and Multivariable Temperature
2.3.2 Single Common Temperature
2.3.3 Generalised Zeroth and First Laws
References
3 Many-Body Quantum Spacetime
3.1 Atoms of Quantum Space and Kinematics
3.2 Interacting Quantum Spacetime and Dynamics
3.3 Generalised Equilibrium States
3.4 Effective Statistical Group Field Theory
References
4 Group Field Theory
4.1 Bosonic Group Field Theory
4.1.1 Degenerate Vacuum and Fock Representation
4.1.2 Useful Bases
4.1.3 Weyl Algebra
4.1.4 Translation Automorphisms
4.2 Deparametrization in Group Field Theory
4.2.1 Classical System
4.2.2 Quantum System
References
5 Thermal Group Field Theory
5.1 Generalised Gibbs States
5.1.1 Positive Extensive Operators
5.1.2 Momentum Operators
5.1.3 Constraint Functions
5.2 Thermofield Doubles, Thermal Representations and Condensates
5.2.1 Preliminaries: Thermofield Dynamics
5.2.2 Degenerate Vacuum and Zero Temperature Phase
5.2.3 Thermal Squeezed Vacuum and Finite Temperature Phase
5.2.4 Coherent Thermal Condensates
5.3 Thermal Condensate Cosmology
5.3.1 Condensates with Volume Fluctuations
5.3.2 Effective Group Field Theory Dynamics
5.3.3 Smearing Functions and Reference Clocks
5.3.4 Relational Functional Dynamics
5.3.5 Effective Cosmology with Volume Fluctuations
5.3.6 Remarks
References
6 Conclusions
6.1 Towards Generalised Equilibrium Statistical Mechanics
6.2 Towards Thermal Quantum Spacetime
6.2.1 Many-Body Formulation and Group Field Theory
6.2.2 Generalised Gibbs States
6.2.3 Thermofield Double Vacua and Inequivalent Representations
6.2.4 Condensate Cosmology with Volume Fluctuations
6.3 Final Remarks
References