Path Integrals in Spherical Coordinates

Pankaj Sharan

Sreya Banerjee, Z. Harman

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.

I. H. Duru, Nuri Ünal

An alternative derivation of the path integrals in spherical coordinates is presented for the purpose of discussing the nature of the quantum mechanical terms appearing in the action. It is shown that the Jacobian resulting from the transformation of the functional measure from cartesian coordinates changes the action by surface terms which then lead to the correct ordering contributions.