  The gauge-boson sector of perturbative scalar electrodynamics is investigated
in detail as a testing ground for resummation methods in hot gauge theories. It
also serves as a simple non-trivial reference system for the non-Abelian gluon
plasma. The complete next-to-leading order contributions to the polarization
tensor are obtained within the resummation scheme of Braaten and Pisarski. The
simpler scheme proposed recently by Arnold and Espinosa is shown to apply to
static quantities only, whereas Braaten-Pisarski resummation turns out to need
modification for collective phenomena close to the light-cone. Finally, a
recently proposed resummation of quasi-particle damping contributions is
assessed critically.
