Exactly solvable dynamical systems in the neighborhood of the Calogero model

Details Exactly solvable dynamical systems in the neighborhood of the Calogero model Exactly solvable dynamical systems in the neighborhood of the Calogero model

1998-03-20

arxiv.org/abs/hep-th/9803169v2

Int.J.Mod.Phys. A14 (1999) 387-408

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 2 figures, replaced and enlarged version

Scientific paper

10.1142/S0217751X99000191

The Hamiltonian of the $N$-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For N=3 and N=4 such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all $N$.

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