Chiral Symmetry Breaking in a Uniform External Magnetic Field

TL;DR

This paper demonstrates that an external magnetic field induces dynamical chiral symmetry breaking in QED at weak couplings and identifies the critical temperature for symmetry restoration, using nonperturbative Schwinger-Dyson equations.

Contribution

It provides a nonperturbative analysis showing magnetic field-induced chiral symmetry breaking and the temperature-dependent restoration in QED.

Findings

Chiral symmetry is broken at weak couplings in a magnetic field.

Restoration of chiral symmetry occurs above a critical temperature.

Critical temperature depends on magnetic field strength and fine structure constant.

Abstract

Using the nonperturbative Schwinger-Dyson equation, we show that chiral symmetry is dynamically broken in QED at weak couplings when an external magnetic field is present, and that chiral symmetry is restored at temperatures above $T_c \simeq \alpha\pi^2/\sqrt{2 \pi |eH|}$, where $\alpha$ is the fine structure constant and $H$ is the magnetic field strength.