Master thesis defense by Carl Jordan Eriksen

Title: Scattering amplitudes from curved space

Abstract: Motivated by the study of extreme mass-ratio binary systems, recent work has explored the use of curved backgrounds in computations of classical gravitational amplitudes [2308.15304, 2308.14832]. While these investigations concern the self-force expansion, the use of curved backgrounds is interesting in its own right. In this thesis, I examine how worldline quantum field theory, combined with an expansion around the Schwarzschild–Tangherlini metric, can be used to reformulate the perturbative expansion of the Compton amplitude, which describes the scattering of a graviton off a compact object.  To formulate this expansion, it is necessary to develop a perturbation theory for the partition function of a worldline coupled to gravity in a curved background, requiring the derivation of curved-space Feynman rules. Having established this framework, I compute the first and second post-Minkowskian contributions to the Compton amplitude. Both are shown to match the results obtained from a flat-space computation. In addition, the second-order amplitude displays the expected infrared behavior and agrees with earlier results on massless gravitational scattering.