Log Soft Constraints on KMOC Formalism

TL;DR

This paper applies the KMOC formalism to electromagnetic scattering in four dimensions, deriving classical memory effects and tail contributions from amplitude data, and establishing consistency conditions related to causality.

Contribution

It introduces a method to compute electromagnetic memory and tail effects within the KMOC formalism using soft-photon theorems, linking infrared observables to S-matrix properties.

Findings

Memory and tail effects derived from amplitude data

Infrared observables connected to soft-photon theorems

Consistency conditions on the S-matrix related to causality

Abstract

The KMOC formalism provides a systematic framework for extracting classical observables perturbatively from on-shell scattering amplitudes. In this work, we apply this formalism to compute electromagnetic observables in four dimensions, focusing in particular on the linear memory effect and its tail contributions. Using the leading and subleading soft-photon theorems to construct the soft radiation kernel, we demonstrate how these infrared observables emerge directly from amplitude data. We further show that demanding the expected non-perturbative properties of memory and tail effects imposes a nontrivial set of consistency conditions on the underlying S-matrix. We interpret these constraints as imposing the requirement of macroscopic causality on the S-matrix via analysis of inclusive observables.