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. * Electronic address: fbrandt@usp.br † Electronic address: dgmckeo2@uwo.ca ‡ Electronic address: apatrus@uwo.ca