CLASSICAL PARTICLES AND THE DIRAC-EQUATION WITH AN ELECTROMAGNETIC-FIELD

The Einstein-Kac lattice model of Brownian motion in one dimension is extended to include massless particles which do not themselves scatter , but which facilitate scattering of Brownian particles, The model is completely classical and no formal quantization is employed. However b y observing second-order effects in the distribution of Brownian parti cles we recover directly the components of Dirac wave functions. Furth ermore the probability densities describing the massless particles are shown to form 'fields' which obey Maxwell's equations. This result ex tends the context of the Dirac equation to include the physics of ense mbles of classical particles with contact interactions. In this contex t all 'quantum objects', including the wave function itself, are obser vable in terms of distributions of particles on a lattice. (C) 1997 El sevier Science Ltd.