tests and applications of Migdal's particle path-integral representation for the Dirac propagator

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.

11.15.Tk
03.70.+k
fermion: Dirac
propagator
dimension: 2
dimension: 3
path integral
anomaly: chiral
gauge field theory: U(1)
Chern-Simons term

References(19)

Figures(0)

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