Free delta propagator

The free propagator for the spin $\frac{3}{2}$, isospin $\frac{3}{2}$ (delta) particle is discussed, comparing the Rarita-Schwinger formalism and another of Hayward. Its use in the calculation of resonant graphs in pion-nucleon scattering, photon-nucleon scattering, and pion photoproduction from nucleons is exemplified using explicit formulae and numerical results. Predictions using the two formalisms are shown to be in significant disagreement.