The Modification of Feynman Diagrams in Curved Space-Time

This paper explores the behavior of quantum particles in weak gravitational fields. We examine scalar and spinor particles, showing that these quantum particles in weak gravitational fields follow geodesic trajectories, aligning with classical expectations. Further, we explore the impact of gravitational fields on Yukawa interaction $\lambda \bar{\mathrm{\Psi }}\mathrm{\Phi }\mathrm{\Psi }$, revealing that Feynman diagrams are modified due to the curvature, affecting propagators and interaction dynamics. The presence of spatially-dependent factors in propagators underscores the localized nature of gravitational effects on particle interactions.