Bodeker's effective theory: From Langevin dynamicsto Dyson-Schwinger equations

摘要

The dynamics of weakly coupled, non-abelian gauge fields at hightemperature is non-perturbative if the characteristic momentumscale is of order IK|~g~2T. Such a situation is typical for the pro-cesses of electroweak baryon number violation in the early Uni-verse. Bodeker has derived an effective theory that describes thedynamics of the soft field modes by means of a Langevin equation.This effective theory has been used for lattice calculations so far[G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: : G.D. Moore, Phys. Rev. D62 (2000) 085011. Availablefrom: l. In this work we provide a complemen-tary, more analytic approach based on Dyson-Schwinger equa-tions. Using methods known from stochastic quantitation, werecast Bodeker's Langevin equation in the form of a field theoreticpath integral. We introduce gauge ghosts in order to help controlpossible gauge artefacts that might appear after truncation, andwhich leads to a BRST symmetric formulation and to correspondingWard identities. A second set of Ward identities, reflecting the ori-gin of the theory in a stochastic differential equation, is alsoobtained. Finally, Dyson-Schwinger equations are derived.