= Massive Rarita-Schwinger constraints
{title2=$\gamma\cdot\psi=\partial\cdot\psi=0$}
For $\gamma^{\mu\nu\rho}\partial_\nu\psi_\rho-m\gamma^{\mu\rho}\psi_\rho=0$ with $m\ne0$, divergence gives $\gamma^{\mu\rho}\partial_\mu\psi_\rho=0$. Gamma contraction then forces $\gamma\cdot\psi=0$, hence $\partial\cdot\psi=0$. The remaining equation is $(\not\partial+m)\psi_\mu=0$ in a mostly-plus convention. In the rest frame the temporal component vanishes, leaving a spatial <vector> times an on-shell two-component spinor; its gamma trace removes the spin-one-half sector. The remaining spin-three-halves representation has four physical states, including longitudinal helicities $\pm1/2$.
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