New Frontiers of Quantum Field and Gravity

Gravitational radiation from the scattering of two compact objects can be computed directly from scattering amplitudes within the observable-based (KMOC) formalism. In this approach, the waveform in frequency space is obtained from Fourier integrals of radiative 2→3 scattering amplitudes. In this talk, I focus on the analytic and algebraic structure of these Fourier integrals and show how they belong to the mathematical class of twisted period integrals. I explain how they exhibit a finite-dimensional vector-space structure and satisfy linear and quadratic relations, as well as systems of differential equations in the kinematic invariants. Using these techniques, we compute for the first time the fully analytic next-to-leading order (NLO) gravitational radiation at all orders in velocity. This framework provides a systematic and extensible pathway towards higher-precision gravitational-wave predictions, including higher perturbative orders and the inclusion of spin effects. The activity was carried out within the project: NOTIMEFORCOSMO "No time for cosmology: Decoding dynamics from static cosmological correlations", Grant Agreement 101126304, CUP E53C23002380006