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arXiv · hep-th/0102153

Quadratic Algebra associated with Rational Calogero-Moser Models

R. Caseiro·J. -P. Francoise·R. Sasaki
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Abstract

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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R. Caseiro, J. -P. Francoise, R. Sasaki. 2001-02-22. Quadratic Algebra associated with Rational Calogero-Moser Models. https://doi.org/10.1063/1.1404387

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