Abstract :
The dynamics of soft (|p|∼g2T) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft scale is determined by diagrams with external momenta p0≲g2T, |p|∼g2T and loop momenta larger than g2T. 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 the gauge coupling g. The transversality indicates that this approach leads to a gauge invariant effective theory.
