arXiv 0811.14912008-11-10hep-phhep-th

博德克的有效理论：从朗之万动力学到戴森-施温格方程

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

Claus Zahlten, Andres Hernandez, Michael G. Schmidt

备注：: 56 pages
发表信息：: Annals Phys.324:2108-2145,2009
DOI：: 10.1016/j.aop.2009.04.006

摘要：

如果特征动量标度为|k| ~ g ^2 T，则高温下弱耦合非阿贝尔规范场的动力学是非微扰的。这种情况在早期宇宙的电弱重子数破坏过程中是典型的。博德克推导了一个有效的理论，该理论通过朗之万方程描述了软场模式的动力学。这种有效的理论已被用于晶格计算到目前为止。在这项工作中，我们提供了一个互补的，更多的分析方法的基础上戴森Schwinger方程。使用已知的随机量子化的方法，我们重铸博德克的朗之万方程的形式的场论路径积分。我们引入规范鬼，以帮助控制可能出现的规文物截断后，这导致了BRST对称制定和相应的沃德恒等式。第二套沃德恒等式，反映了起源的理论在随机微分方程，也得到。最后导出了Dyson-Schwinger方程。

英文摘要：

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.

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