Path integral formulation of general diffusion processes

Abstract

A method is given for the derivation of a path integral representation of the Green's function solution P of equations ∂P/∂t=LP, L being some Liouville operator. The method is applied to general diffusion processes. Feynman's path integral representation of the Schrödinger equation and Stratonovich's path integral representation of multivariate Markovian processes are obtained as special cases if the metric of the general diffusion process is flat. For curved phase spaces our result is a nontrivial generalization and new. New applications e.g. to quantized motion in general relativity, to transport processes in inhomogeneous systems, or to nonlinear non-equilibrium thermodynamics are made possible. We expect applications to be fruitfull in all cases where (continuous) macroscopic transport processes in Riemann geometries have to be considered. © 1977 Springer-Verlag.