Records from the S-Matrix Marathon: Asymptotic Observables

TL;DR

This paper introduces the concept of asymptotic observables in quantum field theory, proposing a unified framework relating various measurable quantities through analytic continuation and exploring their properties and applications.

Contribution

It presents a novel unified approach to asymptotic observables, linking different classes via analytic continuation and discussing their analyticity properties and infrared divergence exponentiation.

Findings

Asymptotic observables include scattering amplitudes and inclusive cross sections.

Unified picture relates observables through analytic continuation and crossing symmetry.

Infrared divergences in QED can be exponentiated using time-folded contours.

Abstract

These lectures introduce the notion of asymptotic observables, which are classes of measurable quantities predicted by quantum field theory. In gapped theories with trivial infrared dynamics, these include scattering amplitudes, expectation values of operators approaching infinity, inclusive cross sections, etc. We argue for a unified picture in which various asymptotic observables are related by analytic continuation embodying new versions of crossing symmetry. As an application, we discuss the exponentiation of infrared divergences for inclusive observables in Quantum Electrodynamics using time-folded contours. Finally, we outline prospects for a systematic study of analyticity properties of asymptotic observables using the Fourier-Bros-Iagolnitzer transform. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11-22 March 2024.