Longitudinal subtleties in diffusive Langevin equations for non-Abelian plasmas - art. no. 025007

Bodeker has recently argued that non-perturbative processes in very high te mperature 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. Bodeker's ef fective theory is intended to describe the long-distance transverse electri c and magnetic fields which art: responsible for non-perturbative dynamics. His effective theory, however, also contains long-wavelength longitudinal electric fields. We discuss several subtleties in the treatment of longitud inal dynamics which were not closely examined in Bodeker's original treatme nt. Somewhat to our surprise, we find that within its domain of validity Bo deker's effective theory does correctly describe both longitudinal and tran sverse fluctuations. We also show that, as far as the transverse dynamics o f interest is concerned, Bodeker's effective theory could be replaced by a transverse-only theory that removes the longitudinal dynamics altogether. I n the process, we discuss several interesting aspects of stochastic field t heories. [S0556-2821(99)01012-7].