Smoothness of Classical Limit in KMOC Formalism

TL;DR

This work extends the KMOC program by embedding the S-matrix in exponential form, $S = e^{iN/\hbar}$, to prove that the classical limits of inclusive observables are free of superclassical divergences to all orders. By organizing contributions through the recursive operators $A_n^O$ and exploiting tree-level scaling, the authors show systematic cancellations of inverse-$\hbar$ terms across elastic and inelastic channels, including static modes, for the linear impulse, angular impulse, and radiation observables. They generalize previous elastic-channel results to inelastic channels and demonstrate that in the electromagnetic scattering of scalars the radiative field and angular impulse have smooth $\hbar \to 0$ limits, with any potential superclassical terms canceled or rendered subleading. The findings bolster the KMOC framework as a robust, universal method for obtaining classical radiative observables from quantum amplitudes, using only terms that scale as $\hbar^0$ and avoiding superclassical divergences.

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.

Figures (1)

• Figure 1: Tree-level diagram with only 3 pt. vertices for $p_1, p_2 \to p_1', p_2', \Upsilon_n^{\vec{r},\vec{\sigma}}$ amplitude