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As I understand it, in the Wheeler-de-Witt formalism you sum over the spaces bounded by a start space and and end space.

What I want to know is where do gravitons fit into this picture?

I understand where they come from in string theory since you have individual strings and particular modes correspond to gravitons.

But in the Wheeler-de-Witt formalism the 3-manifolds for enclosing the histories are considered featureless apart from their curvature.

I'm sure with Kaluza-klein methods or supersymmetry one could add other fields. But how do they quantised? Where does the infinite dimensional Fock space arise in this formalism?

Do gravitons have to be added such as with topological features?

In other words how do we get from this, where g1 and g2 are the bounding 3-manifolds:

$\int_{g1}^{g2} e^{i S[g] } D[g]$

to this where In and Out are the collection of gravitons at the start and end:

$\int e^{i S[g] } In[g] Out[g] D[g]$

Is there any connection?

I read here that even DeWitt himself says that the Wheeler-de-Witt equation is "misplaced" does that mean it's wrong and not compatible with string theory?

I've read other places that the WDW equation can model p-branes but that gravitons are modelled as closed strings attached to p-branes. So it seems that they are an additional feature. Unless p-branes can be modelled as collections of open strings?

  • will this help http://arxiv.org/abs/gr-qc/9711037 – anna v Jun 21 '15 at 15:23
  • as the link I gave gives the prescription for Feynman graphs of the theory, the gravitons are there in the propagators. – anna v Jun 22 '15 at 11:02
  • Well if $\Psi$ is supposed to be the wave function of the Universe. Should the wheeler-de-witt equation be written: $\int \Psi_in[g] \Psi_out[g] e^{iS[\Psi]}$ where S is some action on $\Psi$? This makes it look very similar to the wave function for a membrane in string field theory. $\Psi$ is the membrane field and g is the membrane metric. S would be something like $\Psi(\frac{\delta}{\delta g}\frac{\delta}{\delta g} - R)$\Psi$ –  Jun 22 '15 at 11:14
  • @anna I don't understand that paper. Is it peer reviewed? –  Jun 22 '15 at 11:26
  • It is published in Nuclear Physics B so it is peer reviewed. I cannot answer you . If you do not get a theorist to answer you here, try asking at http://www.physicsoverflow.org/questions/main where it is a mainly theoretical higher level stie – anna v Jun 22 '15 at 12:26

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