Three-body Generalizations of the Sutherland Problem

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dc.creatorQuesne, C.
dc.date1997-06-10
dc.date.accessioned2026-07-07T09:14:38Z
dc.date.available2026-07-07T09:14:38Z
dc.descriptionThe three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is shown to be exactly solvable. When written in appropriate variables, its eigenfunctions can be expressed in terms of Jack symmetric polynomials. The exact solvability of the problem is explained by a hidden $sl(3,R)$ symmetry. A generalized Sutherland three-particle problem including both two- and three-body trigonometric potentials and internal degrees of freedom is then considered. It is analyzed in terms of three first-order noncommuting differential-difference operators, which are constructed by combining SUSYQM supercharges with the elements of the dihedral group~$D_6$. Three alternative commuting operators are also introduced.
dc.description10 pages, LaTeX, no figures, communication at the Workshop on Calogero-Moser-Sutherland Models, Montreal, March 10-15, 1997 (to be published in the Proceedings)
dc.identifierhttps://arxiv.org/abs/hep-th/9706067
dc.identifierhttp://arxiv.org/abs/hep-th/9706067
dc.identifierin Calogero-Moser Sutherland Models, eds. J.F. van Diejen and L. Vinet (Springer-Verlag, New York, 2000) pp. 411-420
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152741
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleThree-body Generalizations of the Sutherland Problem
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