High Spins Beyond Rarita-Schwinger Framework

Abstract

We study the eigenvalue problem of the squared Pauli-Lubanski vector, W^{2}, in the Spinor-Vector representation space and derive from it that the -s(s+1)m^{2} subspace with s=3/2, i.e. spin 3/2 in the rest frame, is pinned down by the one sole Klein-Gordon like equation, [ (p^{2}-m^{2})g_{\alpha\beta}-{2/3}p_{\beta}p_{\alpha}- {1/3}(p_{\alpha}\gamma_{\beta}+p_{\beta}\gamma_{\alpha})\not p +{1/3} \gamma_{\alpha}\not p \gamma_{\beta}\not p ] \psi^{\beta}=0. Upon gauging this W^{2} invariant subspace of \psi_{\mu} is shown to couple to the electromagnetic field in a fully covariant fashion already at zeroth order of 1/m and with the correct gyromagnetic factor of g_{s}=\frac{1}{s}. The gauged equation is hyperbolic and hence free from the Velo-Zwanziger problem of acausal propagation within an electromagnetic field at least to that order.