Bodeker's Effective Theory: From Langevin Dynamics to Dyson-Schwinger Equations

Abstract

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.

arXiv comment56 pages

References in corpus (10)

• Effective dynamics of soft non-abelian gauge fields at finite temperature
• A Self-consistent Inclusion of Magnetic Screening for the Quark-Gluon Plasma
• From hard thermal loops to Langevin dynamics
• Mean Field Dynamics in Non-Abelian Plasmas from Classical Transport Theory
• Effective Transport Equations for non-Abelian Plasmas
• Threshhold Singularities and the Magnetic Mass in Hot QCD
• The Sphaleron Rate: Bodeker's Leading Log
• Generalized Stochastic Quantization of Yang-Mills Theory
• Perturbative and non-perturbative aspects of the non-abelian Boltzmann-Langevin equation
• A local Langevin equation for slow long-distance modes of hot non-Abelian gauge fields