We consider time dependent correlation functions of non-Abelian gauge fields at finite temperature. An effective theory for the soft (p ∼ g 2 T ) 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 ∼ g 2 log(1/g)(g 2 T ) 4 . Furthermore, possible consequences for non-perturbative lattice computations of unequal time correlation functions are discussed.

In extensions of the Standard Model with extra scalars, the electroweak phase transition can be very strong, and the bubble walls can be highly relativistic. We revisit our previous argument that electroweak bubble walls can "run away," that is, achieve extreme ultrarelativistic velocities γ ∼ 10 14 . We show that, when particles cross the bubble wall, they can emit transition radiation. Wall-frame soft processes, though suppressed by a power of the coupling α, have a significance enhanced by the γ-factor of the wall, limiting wall velocities to γ ∼ 1/α. Though the bubble walls can move at almost the speed of light, they carry an infinitesimal share of the plasma's energy.

In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultrarelativistic, with the relativistic gamma factor γ = (1 − v 2 wall ) −1/2 growing linearly with the wall's propagation distance. We provide a simple criterion for determining whether the bubble wall "runs away" in this way or if γ approaches a terminal value.

We develop a discrete lattice implementation of the hard thermal loop effective action by the method of added auxiliary fields. We use the resulting model to measure the sphaleron rate (topological susceptibility) of Yang-Mills theory at weak coupling. Our results give parametric behavior in accord with the arguments of Arnold, Son, and Yaffe, and are in quantitative agreement with the results of Moore, Hu, and Müller.

The production rate of heavy Majorana neutrinos is relevant for models of thermal leptogenesis in the early Universe. In the high temperature limit the production can proceed via the 1 ↔ 2 (inverse) decays which are allowed by the thermal masses. We consider new production mechanisms which are obtained by including additional soft gauge interactions with the plasma. We show that an arbitrary number of such interactions gives leading order contributions, and we sum all of them. The rate turns out to be smooth in the region where the 1 ↔ 2 processes are kinematically forbidden. At higher temperature it is enhanced by a factor 3 compared to the 1 ↔ 2 rate.