Smoothness of Classical Limit in KMOC Formalism

TL;DR

This paper proves that the classical limit of certain inclusive observables in the KMOC formalism is smooth and free from divergences at all perturbative orders, supporting its use for classical radiation calculations.

Contribution

We demonstrate the smoothness of the classical limit for scattering angle, radiative field, and angular impulse in the KMOC formalism, confirming its consistency for classical computations.

Findings

Classical limit of observables is smooth at all orders.

Super-classical divergences are absent in the classical limit.

KMOC formalism effectively captures classical radiation contributions.

Abstract

In this paper, we revisit the smoothness of the classical limit of inclusive observables in the formalism developed by Kosower, Maybee and O'Connell (KMOC). Building on the earlier work [1-3], we prove that the classical limit of three classes of inclusive observables, namely scattering angle, radiative field and angular impulse is smooth and does not suffer from any so-called super-classical divergences at all orders in perturbation. Our analysis goes some way in showing that KMOC formalism can be used to compute classical radiation by simply focusing on all the terms that scale as $\hbar^{0}$ as all the terms that scale with inverse power of $\hbar$ vanish.