Dynamical symmetry algebra of the Calogero model
arXiv:hep-th/0105043 · doi:10.1016/S0370-2693(01)00683-9
Abstract
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 ν. In the bosonic case (ν=0) we find the algebra of generators for every N. For ν\neq 0, we explicitly reproduce the finite algebra for the 4-particle model, demonstrating some general features of our construction.
10 pages, minor corrections, to appear in PLB
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