Finite Temperature and Density Effects in Higher Dimensions with and without Compactifications

TL;DR

This paper derives thermodynamic potentials for Dirac fermions in higher-dimensional spaces at finite temperature and density, analyzing effects of compactification and degeneracy, with implications for models like Candelas-Weinberg.

Contribution

It provides explicit high- and low-temperature expansions of the thermodynamic potential in higher dimensions, including effects of compactification and charge density.

Findings

High temperature and low temperature expansions derived.

Degenerate fermion gas behavior analyzed.

High charge density prevents extra space compactification.

Abstract

Expressions for the thermodynamic potential of a Dirac fermion gas are represented at finite temperature with the chemical potential in an ultrastatic space $R^d\times S^N$. The high- and low- temperature expansions for the thermodynamic potential are obtained and, in particular, strongly degenerate fermi gas is investigated. For the Candelas-Weinberg model, sufficiently high "charge" density prevents the compactification of the extra space.