  Boedeker has recently argued that non-perturbative processes in very high
temperature non-Abelian plasmas (such as electroweak baryon number violation in
the very hot early Universe) can be quantitatively described, to leading
logarithmic accuracy, by a simple diffusive effective theory. Boedeker's
effective theory is intended to describe the long-distance transverse electric
and magnetic fields which are responsible for non-perturbative dynamics. His
effective theory, however, also contains long-wavelength longitudinal electric
fields. We discuss several subtleties in the treatment of longitudinal dynamics
which were not closely examined in Boedeker's original treatment. Somewhat to
our surprise, we find that within its domain of validity Boedeker's effective
theory does correctly describe both longitudinal and transverse fluctuations.
We also show that, as far as the transverse dynamics of interest is concerned,
Boedeker's effective theory could be replaced by a transverse-only theory that
removes the longitudinal dynamics altogether. In the process, we discuss
several interesting aspects of stochastic field theories.
