Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-03-24
Nucl.Phys. B566 (2000) 402-422
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, latex, 4 figures, uses axodraw.sty; discussion of higher loop contributions and of their relation to the Boltzmann e
Scientific paper
The dynamics of soft ($|\vec{p}|\sim g^2 T$) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta $p_0\lsim g^2 T$, $|\vec{p}|\sim g^2 T$ and loop momenta larger than $g^2 T$. We consider the polarization tensor beyond the hard thermal loop approximation, which accounts for loop momenta of order $T$. There are higher loop diagrams, involving also the scale $gT$, which are as important as the hard thermal loops. These higher loop contributions are characteristic for non-Abelian gauge theories and their calculation is simplified by using the hard thermal loop effective theory. Remarkably, the effective one-loop polarization tensor is found to be gauge fixing independent and transverse at leading order in $g$. The transversality indicates that this approach leads to a gauge invariant effective theory.
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