Soft constraints on KMOC formalism

A bstract In this note, we investigate the implications of classical soft theorems for formalism developed by Kosower, Maybee and O’Connell (KMOC) to derive observables in gauge theory gravity from scattering amplitudes. particular, show that radiative electro-magnetic field at leading order expansion imposes an infinite hierarchy constraints on expectation value family generated monomials linear impulse. We perform explicit check these next (NLO) coupling as a corollary how up NLO, radiation obtained quantum amplitudes is consistent with (leading) photon theorem. also argue 4 dimensions log theorem derived Saha, Sahoo Sen generates operators which are products one angular momentum arbitrary number momenta.