Classical Physics and Complete Gravitational Theories from Scattering Amplitudes
Amplitudes methods have been successfully applied to various physical situations. In this manuscript we present their application to two quite distinct problems: classical gravitational-wave physics and constraining gravitational theories beyond general relativity. In chapter 1 we develop two methods for simplifying a computationally intense step in amplitudes calculations, specifically the sum over the physical states of photons and gravitons. These methods, even though generic, are developed with the application of gravitational-wave physics in mind. In chapters 2 and 3 we compute novel corrections to the Newtonian gravitational potential experienced by two spinning objects. These corrections originate in general-relativity effects. In chapter 4 we obtain bounds on Wilson coefficients of four-dimensional gravitational effective field theories. By calculating explicit examples of consistent gravitational theories and extracting the corresponding Wilson coefficients, we find that they occupy tiny islands in the Wilson-coefficient space derived. In chapter 5 we extend this analysis to dimensions higher than four. We again construct explicit gravitational theories and observe that the corresponding Wilson coefficients land in similar regions.