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Quantum energies of GR

  1. Nov 14, 2006 #1
    If we apply the Bohr-Sommerfeld quantization to GR (semiclassical)

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

    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. :frown: :frown:
  2. jcsd
  3. Nov 15, 2006 #2


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    A technical question:
    What is S in your first equation?
    (Obviously, not the same as S in the second one.)
  4. Nov 15, 2006 #3
    Oh..sory "Demystifier"..i forgot to change the letter.. one "S" is the action the other is just to indicate that the integral is performed over a close Hyper-surface on R-4 space (in a similar fashion ot usual WKB formula) i will change it.
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