Reg. Saravi et al., THE ZETA-FUNCTION ANSWER TO PARITY VIOLATION IN 3-DIMENSIONAL GAUGE-THEORIES, International journal of modern physics A, 11(15), 1996, pp. 2643-2660
We study parity violation in (2 + 1)-dimensional gauge theories couple
d to massive fermions. Using the zeta function regularization approach
we evaluate the ground state fermion current in an arbitrary gauge fi
eld 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 classical pa
rity breaking produced by a fermion mass term in three dimensions; the
other, already present for massless fermions, is related to peculiari
ties of gauge-invariant regularization in odd-dimensional spaces.