Thermal Self-Energies Near Zero Four-Momentum

(Talk presented at the 3rd Workshop on Thermal Field Theories and Their Applications, Banff, Canada, August 1993. This is a review of work done with Peter Arnold, Paulo Bedaque, and Ashok Das.) We demonstrate that one-loop self-energies at finite temperature have a unique limit as the external four-momentum goes to zero, as long as the particles propagating in the loop have distinct masses. We show that in spontaneously broken theories, this result nonetheless does not affect the difference between screening and propagating modes and hence the usual resummed perturbation expansion remains unaltered.