F eb 1 99 5 February 1 , 2008 LBL - 35973 Quantum Electrodynamics at Large Distances III : Verification of Pole Factorization and the Correspondence Principle

In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the terms of the remainder are here shown to have singularities on the pertinent Landau singularity surface that are weaker than those of the distinguished part. These remainder terms therefore vanish, relative to the distinguished term, in the appropriate macroscopic limits. This shows, in each order of the perturbative expansion, that quantum electrodynamics does indeed satisfy the pole-factorization and correspondence-principle requirements in the case treated here. It also demonstrates the efficacy of the computational techniques developed here to calculate the consequences of the principles of quantum electrodynamics in the macroscopic and mesoscopic regimes. ∗This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098, and by the Japanese Ministry of Education, Science and Culture under a Grant-in-Aid for Scientific Research (International Scientific Research Program 03044078).