Dynamical symmetry algebra of the Calogero model

Details Dynamical symmetry algebra of the Calogero model Dynamical symmetry algebra of the Calogero model

2001-05-04

arxiv.org/abs/hep-th/0105043v2

Phys.Lett. B511 (2001) 276-284

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, minor corrections, to appear in PLB

Scientific paper

10.1016/S0370-2693(01)00683-9

We study the dynamical symmetry algebra of the N-body Calogero model describing the structure of degenerate levels and demonstrate that the algebra is intrisically polynomial. We discuss some general properties of an algebra of S_N-symmetric operators acting on the S_N-symmetric subspace of the Fock space for any statistical parameter \nu. In the bosonic case (\nu=0) we find the algebra of generators for every N. For \nu\neq 0, we explicitly reproduce the finite algebra for the 4-particle model, demonstrating some general features of our construction.

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