Off-shell phenomena in Coulomb scattering

In the framework of off-shell quantum electrodynamics — the quantum field theory of a covariant symplectic mechanics, in which events evolve according to a Poincaré-invariant parameter τ — we study the low energy scattering of identical scalar particles. It is shown that exchange of mass is permitted in the formalism, and we calculate scattering cross sections for this case. In these cross sections, the usual forward pole of standard scalar QED splits into two poles and a zero, slightly offset from the forward direction. As mass exchange vanishes, a pole-zero pair cancel, the remaining pole moves to θ = 0, and the standard cross section is recovered.