English

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 n=3n=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.

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}
}