A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure

Details A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure

1998-12-17

arxiv.org/abs/hep-th/9812157v1

Int.J.Mod.Phys. A14 (1999) 2993-3004

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 12 pages

Scientific paper

10.1142/S0217751X99001457

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of sl(N+1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry of the parent system is preserved.

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