PoS(IC2006)012 Gauge Symmetries in Fokker-Planck Equations A. E. Santana ∗ Instituto de Física, Universidade de Brasília, 70919-970, Brasília, DF, Brasil E-mail: asantana@fis.unb.br J. A. Cardeal Departamento de Ciências Exatas, Universidade Estadual de Feira de Santana, 44031-460, Feira de Santana, Bahia, Brasil E-mail:cardeal@unb.br F. C. Khanna Theoretical Physics Institute, University of Alberta Edmonton, Alberta, Canada T6G 2J1, TRIUMF, 4004,Wesbrook Mall Vancouver, British Columbia, Canada V6T 2A3 E-mail: khanna@phys.ualberta.ca M. de Montigny Campus Saint-Jean, University of Alberta 8406-91 Street, Edmonton, Alberta, Canada T6C 4G9; Theoretical Physics Institute, University of Alberta Edmonton, Alberta, Canada T6G 2J1 E-mail: montigny@phys.ualberta.ca T. M. Rocha Filho Instituto de Física, Universidade de Brasília 70919-970, Brasília, DF, Brasil E-mail: marciano@fis.unb.br In this work we review some aspects of a metric approach to Galilean invariance to construct equations of Fokker-Planck type with the content of a gauge theory. The metric formalism is based on the projection from an extended (4 + 1) Minkowski manifold to the usual (3 + 1) New- tonian space-time. Whilst the symmetry U (1) gives rise to the usual Fokker-Planck equation, the extension for a nonabelian gauge theory provides us with a Fokker-Planck dynamics including color indices. As an application a non-stationary color-like Ornstein-Uhlenbeck process is stud- ied. In order to derive explicit expression for the drift and diffusion terms, we use an approach based on the theory of Lie algebras for differential equations, working in (1 + 1) space-time. The formalism is presented in detail with three-dimensional Lie algebras. Fifth International Conference on Mathematical Methods in Physics — IC2006 April 24-28 2006 Centro Brasilerio de Pesquisas Fisicas, Rio de Janeiro, Brazil ∗ Speaker. c  Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/