Classical observables from partial wave amplitudes

A bstract We study the formalism of Kosower-Maybee-O’Connell (KMOC) to extract classical impulse from quantum amplitude in context partial wave expansion a 2-to-2 elastic scattering. take two complementary approaches establish connection. The first one takes advantage Clebsch-Gordan relations for base amplitudes expansion. second is novel adaptation traditional saddle point approximation semi-classical limit. In former, an interference between S-matrix and its conjugate leads large degree cancellation such that handle rapidly oscillating integral no longer needed. As example with non-orbital angular momentum, we apply our methods charge-monopole scattering problem probe limit reproduce both angles characterizing spinor basis expansion, non-relativistic avatar spinor-helicity variables, plays crucial role throughout computations.