Scattering theory for quantum electrodynamics. II. Reduction and cross-section formulas

The quantum-electrodynamical S matrix is obtained as the set of on-mass-shell values of the renormalized momentum-space Green's functions multiplied by Ci(mi2-pi2)1+i for each particle i, where i is proportional to the fine-structure constant and Ci is a constant. A photon mass is not needed to eliminate virtual infrared divergences. Instead the parameters i=mi2-pi2 regularize Feynman integrals in the infrared region, and the dependence on the i is canceled against the expansion of (mi2-pi2)i multiplying lower-order Green's functions. Exact cross-section formulas are developed which express transition rates in terms of this S matrix. They account for radiation damping nonperturbatively, whereas the S matrix must be calculated perturbatively as a power series in. It is seen that in processes with very small energy loss to unobserved photons individual elements of the quantum-electrodynamical S matrix are directly observable. Rules for practical calculations are summarized.