Temperature Expansions for Magnetic Systems

TL;DR

This paper develops finite temperature expansions for relativistic fermion systems under magnetic fields and chemical potential, highlighting differences between even and odd dimensions, with a focus on high temperature behavior.

Contribution

It introduces a method combining imaginary-time formalism, proper-time technique, and zeta function regularization to analyze magnetic systems at finite temperature and chemical potential.

Findings

Derived finite temperature expansions for relativistic fermions in magnetic fields.

Highlighted differences between even and odd dimensional systems.

Analyzed high temperature and zero temperature limits with chemical potential.

Abstract

We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the proper-time method for the background field effects, and zeta function regularization for developing the expansions. We emphasize the essential difference between even and odd dimensions, focusing on $2+1$ and $3+1$ dimensions. We concentrate on the high temperature limit, but we also discuss the $T=0$ limit with nonzero chemical potential.