What is interaction Lagrangian of matter and graviton fields

[fxdung]

What is the interaction Lagrangian of matter and graviton fields?So(on the answer)we can say about the nonrenormalization.Why is the divergence of two gravitons diagram able to be the limit of the coincidence of the verties.So we can say about the nonrenormalization.

 

[haushofer]

In writing down the Lagrangian for matter fields, in QFT you use the Minkowski metric. E.g.,the kinetic part of the action of a scalar field contains an inner product. In GR you replace the Minkowski metric by a general metric field which is a solution of the Einstein equations, and partial derivatives become general-covariant ones. These terms contain the interactions between the metric and matter. If you then expand the metric as a perturbation around a vacuum solution, say Minkowski, then you obtain your interaction terms. I don't have experience with calculating such Feynmandiagrams, so maybe some-one else can elaborate on that :)