Final state radiation effects in quantum electrodynamics

This paper establishes the classical causal limit for current-current interactions in Q.E.D., thereby solving a problem which has persisted for over forty years. Once final state radiation effects are allowed for in a non-perturbative manner, it is shown that Q.E.D. describes particles interacting via retarded Lienard--Wiechert potentials; these results are obtained by using Fermi's formulation of the transverse field as a set of quantized oscillators coupled to particle currents, and then by applying functional integration methods to eliminate the intermediate photon coordinates subject to conditions of initial photon vacuum and final photon radiation fields. The first half of the paper shows that specification of initial vacuum and final radiation states holds direct consequences for effective particle interactions. Juxtaposed to these conclusions are the Lamb Shifts and anomalous moment calculations, which are in agreement with experiment; these calculations are conventionally completed without considering final state radiation. If specifcation of final radiation is to affect these radiative correction calculations, then the final numbers to be compared with experiment must not be greatly changed. These considerations comprise the latter half of the work, in which the effects of final state radiation on predicted radiative corrections are demonstrated. Finally, the second half of the paper raises, and to an extent answers, questions related to the problem of building potentials from the exchange of intermediate quanta. Whereas most of the paper deals with Q.E.D., in which the exchanged quanta are photons, the findings of this last section are applicable to all quantum field theories