Grassmann-valued processes for the Weyl and the Dirac equations.

Abstract

The time evolution of a massless particle satisfying the Weyl equation is described as a stochastic process on a space of Grassmann variables, in close formal analogy with the use of Brownian motion for Schr\"odinger evolution. The Grassmann process is then combined with a Poisson process previously used for the evolution of Dirac electrons. (In that process electrons propagate as massless left- or right-handed particles with random changes in direction occurring at an average rate given by the particle mass.) Electron motion is thus given as an expectation over the two processes and spatial position supersymmetrically acquires contributions from sums of products of Grassmann variables.