Non-perturbative aspects of screening phenomena in Abelian and non-Abelian gauge theories

When computed to one-loop order in resummed perturbation theory, the non-abelian Debye mass appears to be logarithmically sensitive to the magnetic scale g(2)T. More generally, we show that in higher orders power-like infrared divergences forbid the use of perturbation theory to calculate the corrections to Debye screening. A similar infrared problem occurs in the determination of the mass-shell behaviour for the scalar propagator in (2+1)-dimensional scalar electrodynamics. In this context, we provide a non-perturbative approach which solves the infrared problems and allows for an accurate calculation of the scalar propagator in the vicinity of the mass shell.