Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-11-10
Annals Phys.324:2108-2145,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
56 pages
Scientific paper
10.1016/j.aop.2009.04.006
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.
Hernandez Andres
Schmidt Michael G.
Zahlten Claus
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