Feynman rules is the basic tool to compute amplitudes in perturbation theory for a QFT. Here, I am trying to understand perturbation theory in GR around the flat space metric, in terms of Feynman rules. There are two basic questions one can ask here :
1) What is the graviton propagator?
2) What is the off shell 3 point function for the GR vertex?
DeWitt has a collection of papers which contain this but the expression for the vertex is slightly obscure and very prone to errors when we expand the symmetrized terms by hand. Hence, can someone please write down the full off shell 3 point vertex explicitly.
Also, he works in the de-Donder gauge, in which the 3 point vertex is sufficiently lengthy. Is there a gauge choice in which the Feynman rules for GR is simpler, and less tedious. Why is the de Donder gauge choice so much more popular in the literature?