Zeta-function regularization and the thermodynamic potential for quantum fields in symmetric spaces

TL;DR

This paper computes the temperature-dependent thermodynamic potential for charged massive quantum fields in symmetric spaces, analyzing low- and high-temperature behaviors and the impact of topology.

Contribution

It introduces a method to evaluate the thermodynamic potential in symmetric spaces, including effects of topology, across temperature regimes.

Findings

Derived low-temperature expansion of the potential

Derived high-temperature expansion of the potential

Identified influence of topology on asymptotic properties

Abstract

We calculate a temperature dependent part of the one-loop thermodynamic potential (and the free energy) for charged massive fields in a general class of irreducible rank 1 symmetric spaces. Both low- and high-temperature expansions are derived and the role of non-trivial topology influence on asymptotic properties of the potential is discussed.