We present an effective field theory of the $Delta$-resonance as an interacting Weinbergs $(3/2,0)oplus (0,3/2)$ 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 $NpiDelta$ and $gammapiDelta$. The proposed framework can be extended to also describe other higher-spin hadronic resonances.
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