High Spins Beyond Rarita-Schwinger Framework

We explicitly construct in the Rarita-Schwinger representation space the operator of the squared Pauli-Lubanski vector and derive from it that the -15/4 m^{2} subspace (spin 3/2 in the rest frame), with well defined parity, is pinned down by the one sole equation, [\epsilon_{\alpha\beta\mu\sigma}\gamma_{5}\gamma^{\mu}p^{\sigma} -m g_{\alpha\beta}]\psi^{\beta}=0. We argue that upon gauging the new equation leads to causal spin-3/2 propagation within an electromagnetic field, thus resolving the Velo-Zwanziger problem