Improved Treatment for the Infrared-Divergence Problem in Quantum Electrodynamics

Abstract

Although the conceptual difficulties associated with infrared divergences in quantum electrodynamics have long since been resolved, a convenient technique for identifying the appropriate infrared-finite part of Feynman graphs has been lacking. Such a technique is presented here. The polarization sums for both real and virtual photons are rearranged into two parts. One of these (called the $K$-polarization sum) resembles a gauge transformation whose structure permits a simple demonstration of infrared factorization and exponentiation. It is easy to see by inspection that the residual factors (with $G$-polarization sums) are infrared free. This is done for each separate graph, in contrast to earlier treatments where contributions from sets of graphs had to be considered together. The technique is illustrated by a detailed treatment of the radiative corrections to lowest-order potential scattering, and generalizations to other processes are indicated.