Stochastic mechanics of a relativistic spinless particle

Abstract

An extension of Nelson’s stochastic mechanics to the relativistic domain is proposed. To each pure state of a spinless relativistic quantum particle corresponds a Markov process t ]ξt, where the random variable ξt represents, at every time t, the space position of the particle in the sense of Newton and Wigner. The process t ]ξt is not a diffusion but the usual Nelson’s theory is restored in the nonrelativistic limit.