Classical gravitational observables from the Eikonal operator

We propose two possible eikonal operators encoding the effects of classical radiation as coherent states gravitons and show how to compute from them different observables. In first proposal, only genuinely propagating are included, while, in second, zero-frequency modes added order recover a static gravitational field. calculate radiated energy-momentum change each particle's momentum, or impulse, 3PM finding agreement with literature. then angular momentum field after collision. do so, we adapt method reverse unitarity presence derivatives describing reproduce result [1] obtained by resumming small-velocity expansion. As new application, derive also variation up 3PM: calculating separately particle contributions allows us check balance laws explicitly. operator encodes linear-response formula Bini-Damour deriving linear radiation-reaction contribution transverse impulse at 4PM.