# Is it possible to define Feynman diagrams in curved space-time?

I have a very simple question:

"Is it possible to talk about Amplitudes and Feynman diagrams assuming a different background than the usual Minkowski one? Let's assume for example that the background is the Schwarzschild one. Is it possible to define an S-matrix for a theory of a scalar particles interacting through gravitons?"

• More on QFT in curved space. – Qmechanic Dec 11 '18 at 18:11
• The answer is completely different depending on whether you want the gravitational field to also be quantized or not. – Javier Dec 11 '18 at 18:16
• I am assuming that the background is the Schwarzschild one, on top of which I am defining a theory of a scalar particle/$\phi$ interacting with gravitons/$h_{\mu \nu}$: in this sense only fluctuations are quantized. – Andrea.Phys Dec 11 '18 at 18:20