Classical observables from coherent-spin amplitudes

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 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.

Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

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Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory

“…However, QFT-based methods suffer a drawback: the need to suppress terms that ultimately disappear in the classical → 0 limit. While the classical limit is now well understood in the non-spinning case as a soft limit [20,34,35,[61][62][63], the situation is further complicated by the need to re-interpret quantized spin degrees of freedom in a classical setting [64][65][66][67]. Nevertheless, these obstacles have been successfully overcome at 2PM order [26,68,69] up to quartic order in spin [70]; other studies of higherspin amplitudes in this context have been done [71][72][73][74][75][76][77][78][79][80][81].…”

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