2020/08/18 by Staneva, Yana
#37J35 (Secondary) #70H06 (Primary) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2008.07765
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.