ζ-function method and the evaluation of fermion currents

Abstract

Using the ζ-function method, a prescription for the evaluation of fermion currents in the presence of background fields is given. The method preserves gauge invariance at each step of the computation and yields to a finite answer showing the relevant physical properties for arbitrary background configurations. Examples for n=2,3 dimensions are worked out, emphasizing the connection between preservation of gauge invariance and violation of other symmetries (chiral symmetry for n=2, parity for n=3).