Path integral representation of the evolution operator for the Dirac equation

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 one to obtain a representation of the path integral over trajectories in the configuration space. This form of the path integral is useful for the formulation of perturbation theory in an external electromagnetic field.