  We compare the effective dynamics of soft fields, based on temperature field
theory, with the mean field dynamics from non-Abelian kinetic theory. We derive
the polarization tensor with the leading logarithmic factor
$\log({gT\over\mu})$ from the effective Boltzmann-Langevin equation given by
Litim and Manuel. The tensor is identical with effective one-loop contributions
within the hard thermal loop effective theory.
