Dirac particle in the presence of plane wave and constant magnetic fields: Path integral approach

TL;DR

This paper computes the Green function for a Dirac particle in combined plane wave and magnetic fields using a path integral approach, introducing identities to simplify integrals and account for classical paths.

Contribution

It introduces a novel application of path integral formalism with constraints to evaluate the Green function in complex electromagnetic field configurations.

Findings

Green function expressed as a Gaussian integral plus classical action

Reduction of integral dimension via introduced identities

Effective classical paths naturally emerge in the formalism

Abstract

The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of path integral via Alexandrou et al. formalism according to the so-called global projection. As a tool of calculation, we introduce two identities (constraints) into this formalism, their main role is the reduction of integrals dimension and the emergence in a natural way of some classical paths, and due to the existence of constant electromagnetic field, we have used the technique of fluctuations. Hence the calculation of the (GF) is reduced to a known gaussian integral plus a contribution of the effective classical action.