The external field approximation of quantum electrodynamics

The quantized field description of particles interacting only with a given unquantized (i.e. external) field is related in a simple way to the one-particle s matrix. Here s is based upon solutions of a one-particle wave equation, without any initial conditions. Thus in the relativistic case, s also acts upon unphysical ''electron'' states of negative energies. A factorization of s leads to simple exact expressions for QED's transition amplitudes for certain electron and/or positron processes (without photons). The formulas involve one-particle matrices, which are given by non-linear equations. The connection between Feynman's general non-unitary sF matrix and the unitary Dirac s matrix is found. A ''radiation interaction picture'' is introduced, and a first order example is given