  In the present paper, we investigate the propagation of a massive
spin-$\frac{3}{2}$ field, aiming at a direct application in hadronic models of
the pion-nucleon ($\pi N$) interaction. Suitable expressions for the
contributions to the standard invariant amplitudes $A$ and $B$ are derived,
applicable in the general case of isospin decomposition. We first deal with the
details of the lengthy calculation involving the Rarita-Schwinger propagator
and confirm the validity of the expressions which had appeared in the
literature in the early 1970s. We subsequently derive the corresponding
contributions when following two other approaches, one featuring the Williams
propagator, the other being known as Pascalutsa's method.
