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

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

1994-11-30

arxiv.org/abs/hep-th/9411238v1

Int.J.Mod.Phys. A11 (1996) 2643-2660

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

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.

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