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arXiv · hep-ph/0202165

From the Dyson-Schwinger to the Transport Equation in the Background Field Gauge of QCD

Q. Wang·K. Redlich·H. Stöcker·W. Greiner
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Abstract

The non-equilibrium quantum field dynamics is usually described in the closed-time-path formalism. The initial state correlations are introduced into the generating functional by non-local source terms. We propose a functional approach to the Dyson-Schwinger equation, which treats the non-local and local source terms in the same way. In this approach, the generating functional is formulated for the connected Green functions and one-particle-irreducible vertices. The great advantages of our approach over the widely used two-particle-irreducible method are that it is much simpler and that it is easy to implement the procedure in a computer program to automatically generate the Feynman diagrams for a given process. The method is then applied to a pure gluon plasma to derive the gauge-covariant transport equation from the Dyson-Schwinger equation in the background covariant gauge. We discuss the structure of the kinetic equation and show its relationship with the classical one. We derive the gauge-covariant collision part and present an approximation in the vicinity of equilibrium. The role of the non-local source kernel in the non-equilibrium system is discussed in the context of a free scalar field.

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Q. Wang, K. Redlich, H. Stöcker, W. Greiner. 2002-10-29. From the Dyson-Schwinger to the Transport Equation in the Background Field Gauge of QCD. https://doi.org/10.1016/s0375-9474(02)01357-x

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