Self-Consistent Dispersion-Theoretic Electromagnetic Scattering Amplitudes

Abstract

A procedure for calculating self-consistent electromagnetic scattering amplitudes when there are bound states, applied in a previous paper to the electron-positron system, is extended to include spin-0-spin-0 and spin-0-spin-$\frac{1}{2}$ elastic scattering. The second-order amplitudes which result have the correct double-spectral functions and are cutoff-independent, analytic, and crossing-symmetric. The Regge trajectory functions which are required by self-consistency imply the usual Coulomb bound-state spectrum with reduced mass and recoil corrections, and the appropriate Regge asymptotic behavior. The correspondence between the amplitudes obtained by this procedure and by other means is discussed briefly.