On the correct propagator for a spin-3/2 particle

Recently a form for the propagator of a spin-3/2 particle has been proposed, which differs from the one normally used in the literature. It is shown that the new propagator gives unique predictions for the contributions to the processes πN→πN, γN→πN, γd→pn from tree diagrams with a Δ(1231) intermediate state, whereas the old propagator gives results which depend on unknown parameters y, z arising from off-mass-shell γNΔ, πNΔ couplings. It is shown further that, with the new propagator, one obtains a very simple model of low-energy pion-nucleon scattering, while the contributions to pion photoproduction and deuteron photodisintegration fit very well into models for these processes. These properties of the new propagator lead the conclusion that it should be used in an effective treatment of Δ exchange, in preference to the usual treatment