The only reference I seem to have to this material is a review article by Duff[*] which states some results of calculations performed using the quantities:

$$\tilde{g}^{\mu\nu}\equiv\sqrt{g}g^{\mu\nu}$$
$$\tilde{g}_{\mu\nu}\equiv\frac{1}{\sqrt{g}}g_{\mu\nu}$$

The graviton field $h^{\mu\nu}$ is defined by a perturbation about flat space $$\tilde{g}^{\mu\nu}=\eta^{\mu\nu}+\kappa h^{\mu\nu}$$ together with the corresponding quantity $$\tilde{g}_{\mu\nu}=\eta_{\mu\nu}-\kappa h_{\mu\nu}+\kappa^2h_{\mu\alpha}h_{\alpha\nu}+...$$ (here $\kappa=\sqrt{16\pi G}$). The free graviton momentum space propagator (after some gauge fixing choices) looks like $$D_{\mu\nu\rho\sigma}(p^2)=\frac{1}{p^2}(\eta_{\mu\rho}\eta_{\nu\sigma}+\eta_{\mu\sigma}\eta_{\nu\rho}-\eta_{\mu\nu}\eta_{\rho\sigma})$$

There are expressions for 3-point, 4-point etc vertices which look rather complicated.

ETA: I found this online reference. The treatment discussing the propagator is around equation (65) onwards. I suspect that there will be much more detail in the original papers of Feynman and de Witt, but I don't have access to them.

[*] M.J.Duff "Covariant Quantization" in Quantum Gravity-an Oxford Symposium. ed Isham, Penrose, Sciama. OUP 1975

This post imported from StackExchange Physics at 2014-03-22 17:22 (UCT), posted by SE-user twistor59