  (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.
