= Second-class constraint
{title2=$\det\{\chi_a,\chi_b\}\ne0$}
A collection of Hamiltonian <constraints> is second class when its <Poisson bracket> matrix $C_{ab}=\{\chi_a,\chi_b\}$ is invertible on the constraint surface. These conditions eliminate canonical variables rather than generate a <gauge symmetry>. Their consistent reduced bracket is the <Dirac bracket>, $\{F,G\}_D=\{F,G\}-\{F,\chi_a\}(C^{-1})^{ab}\{\chi_b,G\}$. The zero temporal <canonical momentum> of a massive <Proca field> and its massive <Gauss law> form such a pair; imposing an independent temporal <canonical commutation relation> would contradict the constraint.
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