Spinning-particle Dirac quantization (${\hat{\zeta }}^m={\gamma }^m/\sqrt{2}$)

Quantizing the odd Dirac brackets yields $\{{\hat{\zeta }}^m,{\hat{\zeta }}^n{\}}_{+}={\eta }^{mn}$. The constraint $p\cdot \zeta =0$ is then the massless Dirac equation on a spinor. Its square enforces $p^2=0$, matching the even constraint. The spin bilinear is represented by $-i[{\gamma }^m,{\gamma }^n]/4$ in this action convention.