Infrared contributions to intermediate state sums in quantum electrodynamics

Abstract

A method has been developed for incorporating the Bloch-Norsdsieck approximation into intermediate state sum expansions in quantum electrodynamics, so as to explicitly include the contributions of soft photons to these sums. This accomplishes the removal of infrared divergences usually incurred in approximations involving the cutting off of such intermediate state sums, and in addition, within the framework of such approximations, gives strong high energy convergence properties to the theory. The formalism developed is applied to modify Fainberg's work on quantum electrodynamic dispersion relations (1). An asymptotic form for the electron's charge form factor is derived, and is shown to be consistent with second order perturbation theory, and a series expansion for the charge renormalization constant Z 3 is obtained, all of whose terms are finite, except for those which arise from states containing only hard photons and no pairs. In a separate development, a comparison is made of the various methods which have been developed for treating the radiative corrections to scattering cross sections due to soft photons.