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For the specified $1/\sqrt{2E_{\mathbf{p}}}$ mode normalization, the canonical anticommutation relations areand every other anticommutator of the $a,b$ operators vanishes. For the Dirac field, they imply the Equal-time canonical anticommutator of a Dirac fieldTo check the normalization, the two sectors contribute $u(\mathbf{p})u^{†}(\mathbf{p})$ and $v(\mathbf{p})v^{†}(\mathbf{p})$ with opposite spatial Fourier signs. Reverse $\mathbf{p}$ in the second contribution. The completeness relations then givewhere $\tilde{p}=(E_{\mathbf{p}},-\mathbf{p})$. This cancels the mode denominator and leaves the Fourier representation of the delta function. Same-momentum $u^{†}v$ orthogonality must not be used in place of this reversed-momentum identity.

For arbitrary spacetime points,For spacelike $z$, choose a Lorentz frame with $z^0=0$; reversing spatial momentum shows $\Delta (z)=0$. Its derivatives vanish there as well, so the field anticommutators vanish at spacelike separation. This is fermionic microcausality. The anticommutation rules make the occupation of each normalized mode zero or one, implementing the Pauli exclusion principle, and make the normal-ordered free Hamiltonian positive for both particle sectors.