- #1
Karlisbad
- 127
- 0
If we apply the Bohr-Sommerfeld quantization to GR (semiclassical)
\oint_{S} \pi _{ab} dg_{ab}=\hbar (n+1/2)
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:
\Psi=e^{iS/\hbar} 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.
\oint_{S} \pi _{ab} dg_{ab}=\hbar (n+1/2)
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:
\Psi=e^{iS/\hbar} 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.