SELF-CONSISTENT RESUMMATION SCHEME IN SCALAR QED

In this paper we derive a resummation scheme that may be useful in the calculation of finite temperature processes that involve infrared-divergent diagrams. We discuss the inclusion of self-consistent vertices in calculations of diagrams with very soft external momenta. We work with scalar QED and show that the use of self-consistent vertices in the infrared limit of the retarded photon polarization tensor is equivalent to the resummation of dominant diagrams. To lowest order in an expansion about the parameter that is to be determined self-consistently, we find that the result is independent of this parameter and equal to the expression obtained with uncorrected lines and vertices. The motivation for this work is the hope that it will be possible to use this technique to perform self-consistent calculations beyond leading order.