Effective action for SU(N) at a finite temperature

Techniques are developed in order to study static magnetic screening and other nonperturbative aspects of QCD at high temperatures. In particular, a covariant derivative expansion of the one-loop effective action is presented and then modified by an infinite resummation so as to provide agreement with the exactly calculable one-loop effective potential. Essential to this technique is a self-consistently defined infrared cutoff which determines the prefactor in semiclassical calculations. Using this prefactor, densities of monopole and dyon plasmas are calculated, and it is found that if such plasmas do exist at finite temperature, then the solitons involved must be overlapping one another. It is also shown that no consistent perturbative or nonperturbative approximation can give rise to a linear term in the SU(2) effective potential, since such a term would not be gauge invariant. Finally, contour plots of the SU(3) A₀ effective potential are presented.