Path integral representation of the evolution operator for the Dirac equation

TL;DR

This paper introduces a new path integral representation for the Dirac equation's evolution operator, enabling better perturbation theory formulation in external fields by regularizing the phase space integral.

Contribution

It presents a regularized path integral formulation over configuration space trajectories for the Dirac equation, facilitating perturbation theory in external electromagnetic fields.

Findings

Regularized path integral over configuration space derived

Representation useful for perturbation theory in external fields

Provides a new mathematical framework for Dirac equation analysis

Abstract

A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase space. This regularization allows to obtain a representation of the path integral over trajectories in the configuration space, i.e. in the Minkowsky space. This form of the path integral is useful for the formulation of perturbation theory in an external electromagnetic field.