quantum field theories dynamically [@Cooper] have been made but the possibilities afforded by these approximations thus far do not allow for the correct description of thermalization processes [@BW] (with the exception of Boltzmann transport theory [@KB]) and have therefore very limited applicability to the description of the long time dynamics of a system undergoing a symmetry breaking phase transition.

In addition a reasonable case can be made that close to a second order transition the theory is effectively at high temperature $T>> m(T)$, where $m(T)$ is the temperature dependent mass scale, and its infrared should behave approximately classically. In this regime some quantum effects can also be included effectively through the appropriate choice of the coupling of the fields to the external environment (the quantum fluctuations in this case) and/or their contributions to the mass and couplings of the dynamical fields. This line of considerations [@Bodeker] has been used recently to describe the effective evolution of the long wave-length modes of the color fields of non-Abelian gauge theories in the high temperature regime, as a stochastic classical field theory.

In cosmology and high energy physics field theories are relativistic. This implies that the time evolution of scalar fields is governed 