  The dynamics of weakly coupled, non-abelian gauge fields at high temperature
is non-perturbative if the characteristic momentum scale is of order |k|~ g^2
T. Such a situation is typical for the processes of electroweak baryon number
violation in the early Universe. Bodeker has derived an effective theory that
describes the dynamics of the soft field modes by means of a Langevin equation.
This effective theory has been used for lattice calculations so far. In this
work we provide a complementary, more analytic approach based on
Dyson-Schwinger equations. Using methods known from stochastic quantisation, we
recast Bodeker's Langevin equation in the form of a field theoretic path
integral. We introduce gauge ghosts in order to help control possible gauge
artefacts that might appear after truncation, and which leads to a BRST
symmetric formulation and to corresponding Ward identities. A second set of
Ward identities, reflecting the origin of the theory in a stochastic
differential equation, is also obtained. Finally Dyson-Schwinger equations are
derived.
