Can a Functional Equation Solve the Problem of Time in Quantum Gravity?

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We have for Quantum gravity the equation:

H|\Psi>=0 as you can see this is time-independent partial differential equation, my question is if we could construct a functional differential equation in the form:

\alpha{d\Psi/dt}+\Beta{H_1}=0 where the H1 would have the derivatives respect to the metric and alpha and beta would be matrices (alpah is a Grassman number) in a way that we would have a functional equation of spin 2 (graviton) with this we would have solved the problem of time in quantum gravity.
 
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