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.

arXiv comment11 pages. Improved version with typos corrected and shortened in one section on alternative approaches. Accepted for publication in PRD

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Cited by in corpus (7)

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• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
• Geometry of spin-field coupling on the worldline
• Euler-Heisenberg Lagrangian under an axial gauge field
• Chirality and parity in a first-quantized representation
• New tests and applications of the worldline path integral in the first order formalism
• Spin in the Worldline Path Integral in 2+1 Dimensions