Quantum electrodynamics at large distances. I. Extracting the correspondence-principle part

In quantum electrodynamics a classical or correspondence-principle part of the S matrix is normally factored out in order to obtain a remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as usually performed, introduces spurious large-distance effects that produce an apparent breakdown of the important correspondence between stable particles and poles of the S matrix, and, in fact, lead to violations of the correspondence principle and to incorrent results for computations in the mesoscopic domain lying between the atomic and classical regimes. A computational technique is developed here that allows valid results to be calculated in this domain. It is shown in this article, and in paper II, in the context of a special example, how to extract a distinguished part of the S matrix that meets the requirements of the correspondence principle, of the pole-particle correspondence, and of infrared finiteness. In paper III the terms of the perturbatively treated remainder are shown to vanish, relative to this distinguished part, in the appropriate macroscopic limits. Thus this work provides both a needed computational technique and a confirmation in quantum electrodynamics of the validity of the correspondence principle and of the pole-particle correspondence, at least in the special case treated here in detail.