QUANTUM ELECTRODYNAMICS AT LARGE DISTANCES .3. VERIFICATION OF POLE FACTORIZATION AND THE CORRESPONDENCE PRINCIPLE

In papers I and II it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets th e correspondence-principle and pole-factorization requirements. The in tegrals that define the terms of the remainder are here shown to have singularities on the pertinent Landau singularity surface that are wea ker than those of the distinguished part. These remainder terms theref ore vanish, relative to the distinguished term, in the appropriate mac roscopic limits. This shows, in each order of the perturbative expansi on, that quantum electrodynamics does indeed satisfy the pole-factoriz ation and correspondence-principle requirements in the case treated he re. It also demonstrates the efficacy of the computational techniques developed here to calculate the consequences of the principles of quan tum electrodynamics in the macroscopic and mesoscopic regimes.