Macrostates thermodynamics and its stable classical limit in Global One-Dimensional Quantum General Relativity

TL;DR

This paper explores a toy model of quantum gravity, demonstrating how its thermodynamics and classical limit align with general relativity through a one-particle density operator approach and Bose-Einstein gas analysis.

Contribution

It introduces a novel quantum gravity toy model and shows its thermodynamic properties converge to classical gravity in the Boltzmann gas limit.

Findings

Thermodynamics of the model matches classical gravity degrees of freedom.

The classical limit is consistent with General Relativity.

The model uses a Bose-Einstein gas of space quantum states.

Abstract

Global One--Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3+1 metric, where the dimension is a volume of three-dimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3+1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose-Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. It confirms that the proposed Quantum Gravity toy model has well-defined classical limit in accordance with classical gravity theory.