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A local Langevin equation for slow long-distance modes of hot non-Abelian gauge fields

Dietrich Bodeker
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Abstract

The effective theory for the dynamics of hot non-Abelian gauge fields with spatial momenta of order of the magnetic screening scale g^2 T is described by a Boltzmann equation. The dynamical content of this theory is explored. There are three relevant frequency scales, g T, g^2 T and g^4 T, associated with plasmon oscillations, multipole fluctuations of color charge, and with the non-perturbative gauge field dynamics, respectively. The frequency scale g T is integrated out. The result is a local Langevin-type equation. It is valid to leading order in g and to all orders in log(1/g), and it does not suffer from the hard thermal loop divergences of classical thermal Yang-Mills theory. We then derive the corresponding Fokker-Planck equation, which is shown to generate an equilibrium distribution corresponding to 3-dimensional Yang-Mills theory plus a Gaussian free field.

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Dietrich Bodeker. 2002-09-06. A local Langevin equation for slow long-distance modes of hot non-Abelian gauge fields. https://doi.org/10.1016/s0370-2693(01)00911-x

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