Chiral and Parity Symmetry Breaking for Planar Fermions: Effects of a Heat Bath and Uniform External Magnetic Field

TL;DR

This paper investigates how chiral symmetry breaking in 2+1-dimensional relativistic fermions is affected by temperature and magnetic fields, revealing two critical temperatures for different condensates and generalizing previous results.

Contribution

It provides a comprehensive analysis of parity-violating fermions under external fields without simplifying assumptions, extending understanding of condensate behavior and related physical quantities.

Findings

Identification of two critical temperatures for condensates.

Reproduction of earlier results in special regimes.

Calculation of magnetization and pair production rate.

Abstract

We study chiral symmetry breaking for relativistic fermions, described by a parity violating Lagrangian in 2+1-dimensions, in the presence of a heat bath and a uniform external magnetic field. Working within their four-component formalism allows for the inclusion of both parity-even and -odd mass terms. Therefore, we can define two types of fermion anti-fermion condensates. For a given value of the magnetic field, there exist two different critical temperatures which would render one of these condensates identically zero, while the other would survive. Our analysis is completely general: it requires no particular simplifying hierarchy among the energy scales involved, namely, bare masses, field strength and temperature. However, we do reproduce some earlier results, obtained or anticipated in literature, corresponding to special kinematical regimes for the parity conserving case. Relating the chiral condensate to the one-loop effective Lagrangian, we also obtain the magnetization and the pair production rate for different fermion species in a uniform electric field through the replacement $B\to-iE$.