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∼g2T) field modes is derived by integrating out the field modes with momenta of order T and of order gT 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 Γ∼g2log(1/g)(g2T)4. Furthermore, possible consequences for non-perturbative lattice computations of unequal time correlation functions are discussed.