Path integral formalism for the free Dirac propagator in spherical coordinates

TL;DR

This paper derives the relativistic Green's function for a free spin-1/2 fermion using path integral formalism in spherical coordinates, providing an exact solution expressed with spherical Bessel functions and spinors.

Contribution

It introduces a coordinate transformation that simplifies the path integral, leading to an exact analytical expression for the Green's function in spherical coordinates.

Findings

Green's function expressed with spherical Bessel functions and spinors

Solution matches previous known results

Method simplifies path integral calculation in spherical coordinates

Abstract

The relativistic Green's function of a free spin-1/2 fermion is derived using the Feynman path integral formalism in spherical coordinates. The Green's function is reduced to an exactly solvable path integral by an appropriate coordinate transformation. The result is given in terms of spherical Bessel functions and spherical spinors, and agrees with previous solutions of the problem.