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A constraint is a condition on the variables of a dynamical problem that the variables (or the physical solution for them) must satisfy. Normally, it amounts to restrictions of such variables to a lower-dimensional hypersurface embedded in the higher-dimensional full space of (unconstrained) variables.
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Dirac procedure for Wheeler De Witt equation
As stated in another response, I think this comes down to a flawed premise, specifically that "the momentum constraints are second-class". They are not. While they are "secondary constraints" to bor …