  We propose two possible eikonal operators encoding the effects of classical
radiation as coherent states of gravitons and show how to compute from them
different classical observables. In the first proposal, only genuinely
propagating gravitons are included, while, in the second, zero-frequency modes
are added in order to recover the effects of a static gravitational field. We
first calculate the radiated energy-momentum and the change in each particle's
momentum, or impulse, to 3PM order finding agreement with the literature. We
then calculate the angular momentum of the gravitational field after the
collision. In order to do so, we adapt the method of reverse unitarity to the
presence of derivatives in the operators describing the angular momentum and
reproduce the result of~\cite{Manohar:2022dea} obtained by resumming the
small-velocity expansion. As a new application, we derive also the variation in
each particle's angular momentum up to 3PM: calculating separately field and
particle contributions allows us to check the balance laws explicitly. We also
show how the eikonal operator encodes the linear-response formula of
Bini-Damour by deriving the linear radiation-reaction contribution to the
transverse impulse at 4PM.

High Energy Physics - Theory;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology