On Generalised Statistical Equilibrium and Discrete Quantum Gravity

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.

Autorentext
Isha Kotecha studied physics and mathematics at Imperial College London and University of Cambridge. She got her PhD in theoretical physics at Max Planck Institute for Gravitational Physics (Albert Einstein Institute), in affiliation with Humboldt University of Berlin. She was a visiting graduate fellow at Perimeter Institute for Theoretical Physics during this time. She is currently a postdoctoral researcher at Okinawa Institute of Science and Technology, and chair at Basic Research Community for Physics, an independent international association of researchers.

Inhalt
Introduction.- Generalised Statistical Equilibrium.- Many-Body Quantum Spacetime.- Group Field Theory.- Thermal Group Field Theory.