Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System

arXiv2008.07765MaRDI QIDQ6347277

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Publication date: 18 August 2020

Abstract: The integrability of the classical and quantum rational Calogero-Moser systems is verified explicitly via the Lax pair method for the case $n=3$. We provide an extensive survey of reflection groups and root systems. The Olshanetsky-Perelomov operators are constructed for a general root system via Dunkl operators, associated to root systems. The integrability of the quantum rational Calogero-Moser system is discussed via the Olshanetsky-Perelomov operators, which provide a set of commuting integrals of motion. The classical analogues of both the Dunkl and the Olshanetsky-Perelomov operators are also presented.

Has companion code repository: https://github.com/yanastaneva8/laxPairs

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