We propose the use of a pure spin-3/2 propagator in the (3/2,0)⊕(0,3/2) representation in particle and nuclear physics. To formulate the propagator in a covariant form we use the antisymmetric tensor spinor representation and we consider the Δ resonance contribution to the elastic πN scattering as an example. We find that the use of a conventional gauge-invariant interaction Lagrangian leads to a problem: the obtained scattering amplitude does not exhibit the resonance behavior. To overcome this problem we modify the interaction by adding a momentum dependence. As in the case of the Rarita-Schwinger formalism, we find that a perfect resonance description could be obtained in the pure spin-3/2 formulation only if hadronic form factors were considered in the interactions.