Superintegrable 3-body systems on the line
Abstract
We consider classical three-body interactions on a Euclidean line depending on the reciprocal distance of the particles and admitting four functionally independent quadratic in the momenta first integrals. These systems are superseparable (i.e. multiseparable), superintegrable and equivalent (up to rescalings) to a one-particle system in the three-dimensional Euclidean space. Common features of the dynamics are discussed. We show how to determine the quantum symmetry operators associated with the first integrals considered here but do not analyze the corresponding quantum dynamics. The conformal superseparability is proved and examples of conformal first integrals are given. The systems considered here in generality include the Calogero, Wolfes, and other three-body interactions widely studied in mathematical physics.
Cite
@article{arxiv.0802.1353,
title = {Superintegrable 3-body systems on the line},
author = {Claudia Chanu and Luca Degiovanni and Giovanni Rastelli},
journal= {arXiv preprint arXiv:0802.1353},
year = {2009}
}
Comments
Corrected typos. Some improvements