Many expositions on canonical quantum gravity start from a 3+1 type formalism, where spacetime is foliated along the time dimension. The Einstein equations then decompose into constraint equations on a hypersurface, and time evolution equations which describe the evolution of the dynamical variables between different slices of the foliaton. For example, equations 4.63 to 4.66 in https://arxiv.org/abs/gr-qc/0703035

I understand that the Hamiltonian associated to the theory is an expression of those constraints, but what happens to equations like 4.63 and 4.64? Is the Wheeler de Witt equation not a complete solution to the problem?


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