Impact of a uniform magnetic field and nonzero temperature on explicit chiral symmetry breaking in QED: Arbitrary hierarchy of energy scales

TL;DR

This paper investigates how a uniform magnetic field and finite temperature influence chiral symmetry breaking in QED, providing general formulas for various energy scale hierarchies and analyzing specific regimes.

Contribution

It offers a comprehensive calculation of the fermion condensate in QED under combined magnetic and thermal effects for arbitrary energy scale hierarchies.

Findings

Derived general expressions for the condensate across different energy regimes.

Reproduced known results in specific limits.

Discussed potential applications of the theoretical findings.

Abstract

Employing the Schwinger's proper-time method, we calculate the $<\bar{\psi} \psi>$-condensate for massive Dirac fermions of charge $e$ interacting with a uniform magnetic field in a heat bath. We present general results for arbitrary hierarchy of the energy scales involved, namely, the fermion mass $m$, the magnetic field strength $\sqrt{eB}$ and temperature $T$. Moreover, we study particular regimes in detail and reproduce some of the results calculated or anticipated earlier in the literature. We also discuss possible applications of our findings.