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 momentum first integrals. These systems are 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 quantum symmetry operators associated with the first integrals considered here but do not analyze the corresponding quantum dynamics. The conformal multiseparability is discussed 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. © 2008 American Institute of Physics.
Chanu, C., Degiovanni, L., Rastelli, G. (2008). Superintegrable 3-body systems on the line. JOURNAL OF MATHEMATICAL PHYSICS, 49(11), 112901 [10.1063/1.3009575].
Superintegrable 3-body systems on the line
CHANU, CLAUDIA MARIA;
2008
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 momentum first integrals. These systems are 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 quantum symmetry operators associated with the first integrals considered here but do not analyze the corresponding quantum dynamics. The conformal multiseparability is discussed 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. © 2008 American Institute of Physics.
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