Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations
- Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)
The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker 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 [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (<hep-ph/9810313>); G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: (<hep-ph/0001216>)]. In this work we provide a complementary, more analytic approach based on Dyson-Schwinger equations. Using methods known from stochastic quantitation, we recast Boedeker'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.
- OSTI ID:
- 21308035
- Journal Information:
- Annals of Physics (New York), Vol. 324, Issue 10; Other Information: DOI: 10.1016/j.aop.2009.04.006; PII: S0003-4916(09)00087-6; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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