= Fermionic bilinear charge algebra
{title2=$[Q_A,Q_B]=Q_{[A,B]},\quad Q_A=\int d^3x:\!\psi^\dagger A\psi\!:$}
For constant internal matrices acting on <Dirac fields>, the equal-time <canonical anticommutation relations> give
$$
[\psi_i^\dagger\psi_j,\psi_k^\dagger\psi_l]=\delta_{jk}\psi_i^\dagger\psi_l-\delta_{il}\psi_k^\dagger\psi_j
$$
with the corresponding spatial delta functions for fields. The quartic terms cancel after fermion reordering. Integrating proves the displayed algebra for well-defined global <Noether charges>, with <normal ordering> and a regulator that preserves the nonanomalous internal symmetry. Orthogonal <chiral projectors> make the left/right mixed commutators zero. This reduces current-charge closure to a finite matrix calculation.
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