论文标题
3维有理calogero-Moser系统的经典和量子整合性的显式计算
Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System
论文作者
论文摘要
经典和量子合理的calogero-moser系统的集成性通过lax对方法明确验证，用于$ n = 3 $。我们提供了对反射组和根系的广泛调查。 Olshanetsky-perelomov操作员是通过与根系相关的DUNKL操作员为一般根系构建的。通过Olshanetsky-perelomov操作员讨论了量子有理Calogero-Moser系统的集成性，该操作员提供了一组通勤的运动积分。还介绍了Dunkl和Olshanetsky-Perelomov操作员的经典类似物。
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.
