What can be measured asymptotically?
Simon Caron-Huot (Department of Physics, McGill University, 3600 Rue University, Montréal, QC, H3A 2T8, Canada, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA); Mathieu Giroux (Department of Physics, McGill University, 3600 Rue University, Montréal, QC, H3A 2T8, Canada); Holmfridur Hannesdottir (Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA); Sebastian Mizera (Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA)
We consider asymptotic observables in quantum field theories in which the S-matrix makes sense. We argue that in addition to scattering amplitudes, a whole compendium of inclusive observables exists where the time-ordering is relaxed. These include expectation values of electromagnetic or gravitational radiation fields as well as out-of-time-order amplitudes. We explain how to calculate them in two ways: by relating them to amplitudes and products of amplitudes, and by using a generalization of the LSZ reduction formula. As an application, we discuss one-loop master integrals contributing to gravitational radiation in the post-Minkowski expansion, emphasizing the role of classical cut contributions and highlighting the different infrared physics of in-in observables.