 Massless Rarita-Schwinger polarization count

Gauge equivalence ${\psi }_{\mu }\sim {\psi }_{\mu }+{\partial }_{\mu }ϵ$ permits gamma-trace gauge. The Rarita-Schwinger field equation then gives transversality and a massless Dirac equation for each component. For momentum along the third axis, residual gauge removes the temporal and longitudinal components. The remaining constraint is ${\psi }_2={\gamma }^1{\gamma }^2{\psi }_1$, with ${\psi }_1$ in the two-dimensional kernel of $/p$. Spinor helicity $\pm 1/2$ is paired with vector helicity of the same sign, leaving only $\pm 3/2$. A Majorana spinor reality condition identifies antiparticles; a Dirac vector-spinor has separate antiparticle modes.