Gauge symmetry in Fokker-Planck dynamics

Using a Galilean metric approach, based on an embedding of the Euclidean space into a (4 + 1)-Minkowski space, we analyze a gauge invariant Lagrangian associated with a Riemannian manifold R, with metric g. With a specific choice of the gauge condition, the Euler-Lagrange equations are written covariantly in R, and then the Fokker-Planck equation is derived, such that the drift and the diffusion terms are obtained from g. The analysis is carried out for both, Abelian and non-Abelian symmetries, and an example with the su(2) symmetry is presented. (C)) 2003 Elsevier Science B.V. All rights reserved.