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{{distinguish|Primary constraint}}
In a constrained Hamiltonian system, a dynamical quantity is called a '''first class constraint''' if its Poisson bracket with all the other constraints vanishes on the '''constraint surface''' (the surface implicitly defined by the simultaneous vanishing of all the constraints). A '''second class constraint''' is one that is not first class.
First and second class constraints were introduced by {{harvs|txt|last=Dirac|authorlink=Paul Dirac|year=1964}} as a way of quantizing mechanical systems such as gauge theories where the symplectic form is degenerate.
==Poisson brackets==
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