Path Integral for the Dirac Equation

TL;DR

This paper develops a path integral formulation for solving the Dirac equation, integrating over real trajectories and variables related to spin and chirality, providing a new mathematical approach.

Contribution

It introduces a c-number path integral representation for the Dirac equation involving real trajectories and spin/chirality variables, a novel formulation.

Findings

Path integral representation for Dirac equation constructed.

Inclusion of spin and chirality variables in the path integral.

Provides a new mathematical framework for Dirac solutions.

Abstract

A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips.