  We present an effective field theory of the $\Delta$-resonance as an
interacting Weinberg's $(3/2,0)\oplus (0,3/2)$ field in the multi-spinor
formalism. We derive its interactions with nucleons $N$, pions $\pi$ and
photons $\gamma$, and compute the $\Delta$-resonance cross-sections in
pion-nucleon scattering and pion photo-production. The theory contains only the
physical spin-3/2 degrees of freedom. Thus, it is intrinsically consistent at
the Hamiltonian level and, unlike the commonly used Rarita-Schwinger framework,
does not require any additional ad hoc manipulation of couplings or
propagators. The symmetries of hadronic physics select a unique operator for
each coupling $N\pi\Delta$ and $\gamma\pi\Delta$. The proposed framework can be
extended to also describe other higher-spin hadronic resonances.
