Effective dynamics of soft non-Abelian gauge fields at finite temperature

We consider time dependent correlation functions of non-abelian gauge fields at finite temperature. An effective theory for the soft (p similar to g(2)T) field modes is derived by integrating out the field modes with momenta of order T and of order T in a leading logarithmic approximation. In this effective theory the time evolution of the soft fields is determined by a local Langevin-type equation. As an application, the rate for hot electroweak baryon number violation is estimated as Gamma similar to g(2)log(1 / g)(g(2)T)(4). Furthermore, possible consequences for non-perturbative lattice computations of unequal time correlation functions are discussed. (C) 1998 Elsevier Science B.V, Ali rights reserved.