Quantum Dynamics as a Stochastic Process

Abstract

We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model is obtained. The resulting theory is similar to Quantum Mechanics, having the same field equations for probability measures, the same operator structure and symmetric ordering of operators. The model is valid for general electromagnetic interaction as well as many body systems with mutual interactions of general nature.