Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field

Abstract

A rigorous path integral representation of the solution of the Cauchy problem for the pure-imaginary-time Schrodinger equation ϖ t ψ(t, x)=−[H−mc 2]ψ(t,x) is established.H is the quantum Hamiltonian associated, via the Weyl correspondence, with the classical Hamiltonian [(cp−eA(x))2+m 2 c 4]1/2+eΦ(x) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Levy process.