  The correspondence principle is important in quantum theory on both the
fundamental and practical levels: it is needed to connect theory to experiment,
and for calculations in the technologically important domain lying between the
atomic and classical regimes. Moreover, a correspondence-principle part of the
S-matrix is normally separated out in quantum electrodynamics in order to
obtain a remainder that can be treated perturbatively. But this separation, as
usually performed, causes an apparent breakdown of the correspondence principle
and the associated pole-factorization property. This breakdown is spurious. It
is shown in this article, and a companion, in the context of a special case,
how to extract a distinguished part of the S-matrix that meets the
correspondence-principle and pole-factorization requirements. In a second
companion paper the terms of the remainder are shown to vanish in the
appropriate macroscopic limits. Thus this work validates the correspondence
principle and pole factorization in quantum electrodynamics, in the special
case treated here, and creates a needed computational technique.
