The Born regime of Gravitational Amplitudes

This talk will be about scattering in the regime where the wavelength of the scattered objects is comparable to their distance but is much larger than any Compton wavelength in the quantum field theory. This is a regime relevant for non-relativistic quantum mechanics but also for classical scattering of gravitational waves. I will argue that in this regime the Feynman diagram expansion reduces to a geometric Born series of some theory-dependent wave equation. In the case of gravity I will show evidence that this wave equation is the Teukolsky equation. I will explore in detail this link between Feynman diagrams and wave equations, and its possible applications. For example, how it can be used to determine the Love numbers of black holes and neutron stars, or to compute radiative corrections to bound states such as positronium or the Hydrogen atom. Based on previous and ongoing work with S. Caron-Huot, G. Isabella and M. Solon.