  The dynamics of soft ($|\vec{p}|\sim g^2 T$) non-Abelian gauge fields at
finite temperature is non-perturbative. The effective theory for the soft
fields can be obtained by first integrating out the momentum scale T, which
yields the well known hard thermal loop effective theory. Then the latter is
used to integrate out the scale gT. One obtains a Boltzmann equation, which can
be solved in a leading logarithmic approximation. The resulting effective
theory for the soft fields is described by a Langevin equation, and it is well
suited for non-perturbative lattice simulations.
