The $ζ$-function answer to parity violation in three dimensional gauge theories

R. E. Gamboa Saravi, G. L. Rossini, F. A. Schaposnik

Published 1994-11-30Version 1

We study parity violation in $2+1$-dimensional gauge theories coupled to massive fermions. Using the $\zeta$-function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern-Simons term in the gauge-field effective action. One is related to the well-known {\em classical} parity breaking produced by a fermion mass term in 3 dimensions; the other one, already present for massless fermions, is related to peculiarities of gauge invariant regularization in odd-dimensional spaces.