What can be measured asymptotically?

Abstract

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.

Equating extrapolate dictionaries for massless scattering

“…Indeed our discussion of how the 3D dictionary relates to the 4D construction of the 𝑆-matrix seemed to also hint at this in connection to certain simple time contours, e.g. in the camera story in [56] as opposed to the more complicated ones related to crossing in [66]. It would be interesting to explore this further and understand what 𝑆 † 𝑆 = 1 looks like from this cylinder perspective or from embedding space.…”