Content deleted Content added
→Examples: Merge from Second class constraints |
Expanding article |
||
Line 7:
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|loc=p.17}} as a way of quantizing mechanical systems such as gauge theories where the symplectic form is degenerate.
The terminology of first and second class constraints is confusingly similar to that of [[primary constraint|primary and secondary constraints]]. These divisions are independent: both first and second class constraints can be either primary or secondary, so this gives altogether four different classes of constraints.
==Poisson brackets==
| |||