Superintegrable 3-body systems on the line

Details Superintegrable 3-body systems on the line Superintegrable 3-body systems on the line

2008-02-10

arxiv.org/abs/0802.1353v4

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Corrected typos. Some improvements

Scientific paper

10.1063/1.3009575

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.

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