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Abstract: We consider classical three-body interactions on a Euclidean line dependingon the reciprocal distance of the particles and admitting four functionallyindependent quadratic in the momenta first integrals. These systems aresuperseparable i.e. multiseparable, superintegrable and equivalent up torescalings to a one-particle system in the three-dimensional Euclidean space.Common features of the dynamics are discussed. We show how to determine thequantum symmetry operators associated with the first integrals considered herebut do not analyze the corresponding quantum dynamics. The conformalsuperseparability is proved and examples of conformal first integrals aregiven. The systems considered here in generality include the Calogero, Wolfes,and other three-body interactions widely studied in mathematical physics.



Autor: Claudia Chanu, Luca Degiovanni, Giovanni Rastelli

Fuente: https://arxiv.org/







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