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

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SUMMARY

The discussion centers on the potential of a functional differential equation to address the problem of time in quantum gravity. The proposed equation is α(dΨ/dt) + βH₁ = 0, where H₁ incorporates derivatives with respect to the metric, and α is a Grassmann number matrix. This formulation aims to create a functional equation of spin 2, representing the graviton, thereby offering a solution to the time issue in quantum gravity. The conversation also suggests engaging with a related thread on Physics Forums for further insights.

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  • Basic principles of metric tensors in physics
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The discussion is beneficial for theoretical physicists, researchers in quantum gravity, and students interested in advanced mathematical physics concepts.

eljose
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We have for Quantum gravity the equation:

[tex]H|\Psi>=0[/tex] 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:

[tex]\alpha{d\Psi/dt}+\Beta{H_1}=0[/tex] 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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