Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System
Mathematical Physics
2020-08-19 v1 math.MP
Abstract
The integrability of the classical and quantum rational Calogero-Moser systems is verified explicitly via the Lax pair method for the case . 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.
Keywords
Cite
@article{arxiv.2008.07765,
title = {Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System},
author = {Yana Staneva},
journal= {arXiv preprint arXiv:2008.07765},
year = {2020}
}