Functional Integral in terms of the Field Strength: An Approach to Chiral Symmetry Breaking

TL;DR

This paper introduces a novel path integral approach using the field-strength tensor to analyze chiral symmetry breaking in 4D QED with four-fermion interactions, revealing spontaneous symmetry breaking for all nonzero couplings.

Contribution

It presents a new integral formulation that simplifies inclusion of higher-order gauge effects in studying chiral symmetry breaking.

Findings

Chiral symmetry is spontaneously broken for any nonzero gauge and four-fermion couplings.

The approach allows calculation of the effective potential up to sixth order.

Higher-order gauge effects can be systematically included in the analysis.

Abstract

The chiral symmetry breaking in the 4-dimensional QED with the chirally invariant four-fermion interaction is discussed by using a novel path integral expression in terms of the field-strength tensor. In the local potential approximation, we find that the chiral symmetry is spontaneously broken for any nonzero gauge and four-fermion couplings on the tree level of an auxiliary field $\sigma$. The present approach allows us to easily include higher orders of the gauge coupling so that the effective potential up to the sixth order is obtained.