ELECTRODYNAMICS IN A BACKGROUND CHIRAL FIELD

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.