A representation of the Belavkin equation via Feynman path integrals (Q1400826)

In 1989 Belavkin proposed a stochastic partial differential equation obtained from the Schrödinger equation by adding a Brownian motion (white noise) term to account for the interaction with the measuring device. The subject is known as continuous measument theory in the literature. A representation of the solution of Belavkin's equation in terms of an oscillatory (i.e., Fresnel type) Feynman path integral is given using the Cameron-Martin formula, and it is shown that the integral corresponds to a stochastic Mehler kernel.