Bose-Einstein condensation as symmetry breaking in compact curved spacetimes

TL;DR

This paper investigates Bose-Einstein condensation in the Einstein static universe, revealing that symmetry breaking does not occur due to the chemical potential never reaching its critical value, with implications for finite-volume spaces.

Contribution

It demonstrates the absence of symmetry breaking in Bose-Einstein condensation within the Einstein static universe and clarifies the connection between statistical mechanics and field theory methods.

Findings

Symmetry breaking does not occur in the Einstein static universe.

The chemical potential never reaches its critical value.

Clarification of the relationship between statistical mechanics and field theory approaches.

Abstract

We examine Bose-Einstein condensation as a form of symmetry breaking in the specific model of the Einstein static universe. We show that symmetry breaking never occursin the sense that the chemical potential $\mu$ never reaches its critical value.This leads us to some statements about spaces of finite volume in general. In an appendix we clarify the relationship between the standard statistical mechanical approaches and the field theory method using zeta functions.