Classical observables from coherent-spin amplitudes

TL;DR

This paper extends the quantum field-theoretic approach to classical observables to include spinning objects using coherent spin states, deriving key scattering and Hamiltonian results for spinning two-body systems.

Contribution

It introduces a covariant formalism for classical spinning objects using coherent spin states within the quantum field theory framework, applicable to two-body scattering.

Findings

Derived classical impulse and spin kick at first post-Minkowskian order

Extracted an effective two-body Hamiltonian for spinning objects

Reproduced classical observables via Hamiltonian equations in the center-of-mass frame

Abstract

The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O'Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group ${\rm SU}(2)$ and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton's constant.