Tests and applications of Migdal's particle path-integral representation for the Dirac Propagator

Abstract

We derive some non-perturbative results in 1+1 and 2+1 dimensions within the context of the particle path-integral representation for a Dirac field propagator in the presence of an external field, in a formulation introduced by Migdal in 1986. We consider the specific properties of the path-integral expressions corresponding to the 1+1 and 2+1 dimensional cases, presenting a derivation of the chiral anomaly in the former and of the Chern-Simons current in the latter. We also discuss particle propagation in constant electromagnetic field backgrounds.

11 pages. Improved version with typos corrected and shortened in one section on alternative approaches. Accepted for publication in PRD