If we apply the Bohr-Sommerfeld quantization to GR (semiclassical)(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \oint_{S} \pi _{ab} dg_{ab}=\hbar (n+1/2) [/tex]

In this case if "Energies" (or whatever you call energy since in Quantum GR H=0 for the "Hamiltonian constraint" ) then using Einstein equation we see that the "curvature" (quantum version) can't be arbitrary (curvature of the surface is quantizied) and that the WKB wave function would be:

[tex] \Psi=e^{iS/\hbar} [/tex] of course the question there is if we can get the action S from the HIlbert-Einstein Lagrangian, or if the WKB method for energies and wavefunctions applied here.

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# Quantum energies of GR

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