Electrodynamics in a Background Chiral Field

TL;DR

This paper derives an exact expression for the one-loop effective action in four-dimensional Euclidean space with a background chiral field, especially for massless spinors, and discusses perturbative approaches for massive cases and analogous two-dimensional problems.

Contribution

It provides an exact formula for the effective action with massless spinors and develops perturbative methods for massive cases in a background chiral field.

Findings

Exact effective action for massless spinors in 4D

Perturbative expansion for massive spinors

Analysis of the 2D analogous problem

Abstract

We consider the one loop effective action in four dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass $m$ of the spinor vanishes. If $m$ does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.