High temperature QCD and QED with unstable excitations

Abstract

We consider the partition functions of QCD and QED at high temperature assuming small coupling constants, and present arguments in favor of an improved perturbative expansion in terms of unstable excitations. Our effective propagators are derived from spectral functions with a constant width. These spectral functions describe screening and damping of gluons (photons) as well as ``Brownian'' motion of quarks (electrons). BRST-invariance allows us to reduce the number of independent width parameters to three. These are determined in a self-consistent way from the one-loop self energy and polarization tensor in the infrared limit thus rendering this limit finite. All spectral width parameters are found to be proportional to $g T$. We reproduce the well known expression for the electric ``Debye''-screening mass. The transverse (magnetic) gluons (photons) are found to interact only at nonzero momentum or energy, at least to leading order. As a consequence their spectral function acquires a width only away from the infrared limit. Finally, plasmon modes are determined and found to be strongly damped.