Quadratic Algebra associated with Rational Calogero-Moser Models

Details Quadratic Algebra associated with Rational Calogero-Moser Models Quadratic Algebra associated with Rational Calogero-Moser Models

2001-02-22

arxiv.org/abs/hep-th/0102153v1

J.Math.Phys. 42 (2001) 5329-5340

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX2e, no figures

Scientific paper

Classical Calogero-Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an additional set of r-1 algebraically and functionally independent globally defined conserved quantities. At the quantum level, Kuznetsov uncovered the existence of a quadratic algebra structure as an underlying key for superintegrability for the models based on A type root systems. Here we demonstrate in a universal way the quadratic algebra structure for quantum rational Calogero-Moser models based on any root systems.

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