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The first-order fermionic kinetic term produces second-class momentum constraints. After eliminating them, the canonical graded Dirac brackets arewith other mixed brackets zero. The bracket of two odd variables is symmetric, consistently with the graded Poisson bracket. The constraint algebra isIt is the worldline supersymmetry algebra: the square of the fermionic constraint generates the Hamiltonian constraint.

With $\hslash =1$, quantization converts these toRepresent the fermions by Gamma matrices, ${\hat{\psi }}^m={\gamma }^m/\sqrt{2}$, where $\{{\gamma }^m,{\gamma }^n{\}}_{+}=2{\eta }^{mn}$, and ${\hat{p}}_m=-i{\partial }_m$. The wavefunction is a Dirac spinor. Its physical-state constraint iswhich is exactly the massless Dirac equation. Moreover ${\hat{\mathcal{Q}}}^2=\hat{\mathcal{H}}=-{\square }_D/2$, so this equation implies the remaining mass-shell constraint. Conversely, a solution of the massless Dirac equation satisfies both constraints. The Klein-Gordon constraint alone would not impose the spinorial first-order equation.