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In this thesis we elaborate on two different aspects of the Effective FieldTheory (EFT) approach to a Binary Coalescing system in General Relativity (GR).First, we consider the issue of hereditary effects in the Post-Newtonian (PN)perturbative scheme, and we compute hereditary diagrams in the far zone regionup to 5PN order, using both Feynman and Schwinger-Keldysh formalism, comparingour results with those appearing in literature. Then, we focus on thePost-Minkowskian (PM) perturbative scheme, and we compute the bending angle ofa massless scalar field under the influence of a massive scalar in the EFT ofGR, up to one loop order in dimensional regularisation. Our analysis points tothe existence of relevant terms that were not accounted for in previous study,which may modify the predictions for physical observables.

Effective Field Theory Approach to General Relativity and Feynman Diagrams for Coalescing Binary Systems