Can Schwinger-Dyson Equations Compute Green Functions in Quantum Gravity?

[Karlisbad]

A question about them (i have looked it up at wikipedia) Can they produce (a solution to them) a way to compute "Green functions" (and hence the propagator) in an "exact" (Non-perturbative approach) way?? .. for example the S-D equation read:

$$\frac{\delta S}{\delta \phi(x)}[-i \frac{\delta}{\delta J}]Z[J]+J(x)Z[J]=0$$ (1)

Then if we put the action S to be $$S[\phi]=\int d^{4}xL_{E-H}$$

where L is the Einstein-Hilbert Lagrangian..a solution to (1) if exist would be a form to compute the Green-function for the "Quantum Gravity"?:shy:

 

[dextercioby]

In principle, yes, you can put the HE Lagrangian in the path integral. However, it leads you nowhere, as the quantum theory is not renormalizable. For any interacting theory the path integral is not exactly computable and so neither the Green functions. This comes from the fact that the classical Lagrangian (or even Hamiltonian, if you know how to obtain them) field equations are not linear, besides being a system of coupled PDE-s.

Daniel.