The effective potential of composite fields in weakly coupled QED in a uniform external magnetic field

TL;DR

This paper derives the effective potential for composite fields in weakly coupled QED under a magnetic field, showing how an external magnetic field induces dynamical fermion mass through chiral symmetry breaking.

Contribution

It provides a derivation of the effective potential for composite fields in QED with an external magnetic field, highlighting the mechanism of dynamical mass generation.

Findings

The effective potential has a non-zero minimum indicating chiral symmetry breaking.

External magnetic field induces a non-vanishing fermion mass.

Comparison with Nambu-Jona-Lasinio model shows similarities in symmetry breaking mechanisms.

Abstract

The effective potential for the composite fields responsible for chiral symmetry breaking in weakly coupled QED in a magnetic field is derived. The global minimum of the effective potential is found to acquire a non-vanishing expectation value of the composite fields that leads to generating the dynamical fermion mass by an external magnetic field. The results are compared with those for the Nambu-Jona-Lasinio model.