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Classical observables from partial wave amplitudes
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DOI：10.1007/JHEP06(2023)096.png)
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Abstract
En 中文
We study the formalism of Kosower-Maybee-O'Connell (KMOC) to extract classical impulse from quantum amplitude in the context of the partial wave expansion of a 2-to-2 elastic scattering. We take two complementary approaches to establish the connection. The first one takes advantage of Clebsch-Gordan relations for the base amplitudes of the partial wave expansion. The second one is a novel adaptation of the traditional saddle point approximation in the semi-classical limit. In the former, an interference between the S-matrix and its conjugate leads to a large degree of cancellation such that the saddle point approximation to handle a rapidly oscillating integral is no longer needed. As an example with a non-orbital angular momentum, we apply our methods to the charge-monopole scattering problem in the probe limit and reproduce both of the two angles characterizing the classical scattering. A spinor basis for the partial wave expansion, a non-relativistic avatar of the spinor-helicity variables, plays a crucial role throughout our computations.
Keywords:
Classical Theories of Gravity
Scattering Amplitudes
Solitons Monopoles and Instantons
Journal
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5.5
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3.9W
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13.7W