Diagrammatic approach to soft nonAbelian dynamics at high temperature

) 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.

Note:

23 pages, latex, 4 figures, uses axodraw.sty; discussion of higher loop contributions and of their relation to the Boltzmann equation (Sect. 5) added, several references added, to appear in Nucl. Phys. B

11.10.Wx
11.15.-q
gauge field theory: nonabelian
finite temperature
polarization: tensor
Feynman graph: higher-order

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