Path-integral solutions of the Dirac equation

Abstract

The feasibility of applying the path-integral formalism for solving the Dirac equation is shown in the case of a free particle for which the Dirac propagator is obtained by evaluating an appropriate path integral, directly constructed from the Dirac equation. Furthermore, the propagator for a Dirac electron in a constant magnetic field is indirectly obtained from the propagator of an auxiliary wave equation by evaluating a world-line (space-time path) integral. The spectrum of the Dirac equation is also, in this case, extracted from an auxiliary propagator.