Algebra of the observables in the Calogero model and in the Chern-Simons matrix model

Details Algebra of the observables in the Calogero model and in the Chern-Simons matrix model Algebra of the observables in the Calogero model and in the Chern-Simons matrix model

2002-03-26

arxiv.org/abs/hep-th/0203245v2

Phys.Rev.B66:205313,2002

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, misprints corrected, reference added, final version, to appear in PRB

Scientific paper

10.1103/PhysRevB.66.205313

The algebra of observables of an N-body Calogero model is represented on the S_N-symmetric subspace of the positive definite Fock space. We discuss some general properties of the algebra and construct four different realizations of the dynamical symmetry algebra of the Calogero model. Using the fact that the minimal algebra of observables is common to the Calogero model and the finite Chern-Simons (CS) matrix model, we extend our analysis to the CS matrix model. We point out the algebraic similarities and distinctions of these models.

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