New tests and applications of the worldline path integral in the first order formalism

TL;DR

This paper develops non-perturbative methods using the worldline path integral formalism to calculate propagators and effective actions for various quantum fields in different backgrounds, providing new exact solutions and interpretations.

Contribution

It introduces novel non-perturbative calculations of propagators and effective actions for multiple fields and backgrounds within the worldline formalism, including exact solutions and anomaly conditions.

Findings

Exact propagators for Dirac, scalar, and Proca fields in constant electromagnetic fields.

Long-distance expansion of scalar propagator in spacelike vortex background.

Interpretation of chiral anomaly via path conditions.

Abstract

We present different non-perturbative calculations within the context of Migdal's representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar and Proca fields in the presence of constant electromagnetic fields, for an even-dimensional spacetime. Then we derive the propagator for a charged scalar field in a spacelike vortex (i.e., instanton) background, in a long-distance expansion, and the exact propagator for a massless Dirac field in 1+1 dimensions in an arbitrary background. Finally, we present an interpretation of the chiral anomaly in the present context, finding a condition that the paths must fulfil in order to have a non-vanishing anomaly.