HEP Theory Journal Club

Crossing beyond scattering amplitudes

Mathieu Giroux

McGill

Introduced in the mid-50s, crossing symmetry in interacting quantum field theory suggests that particles and anti-particles traveling back in time are indistinguishable. This perspective has significant practical implications for perturbative computations and for the S-matrix bootstrap. To prove this property rigorously, one needs to show that on-shell observables across different channels are boundary values of the same analytic function. For the simplest cases of 2-to-2 and 2-to-3 scattering, the known non-perturbative proofs rely heavily on physical principles like (micro)causality, locality, and unitarity, but also on a significant amount of several variables complex analysis, which makes their extension to arbitrary multiplicity quite challenging. In this talk, we review recent progress regarding the implications of crossing symmetry in quantum field theory, assuming analyticity. The story begins by asking what can be measured asymptotically in quantum field theory? Among the answers to this question are conventional (time-ordered) scattering amplitudes, but also a whole compendium of inclusive measurements, such as expectation values of gravitational radiation and out-of-time-ordered correlators. We show that these asymptotic observables can be related to one another through new versions of crossing symmetry, and propose generalized crossing relations together with the corresponding paths of analytic continuation. Throughout the talk, we show how to apply crossing between different observables in practice, both at tree- and loop-level. (Based on: 2308.02125 and 2310.12199)