经典力学和量子力学中的耦合常数变态和N阶对称性
Coupling constant metamorphosis and Nth order symmetries in classical and quantum mechanics
摘要：
我们回顾了耦合常数变态（CCM）和Stäckel变换的基本原理，并应用它们将所有阶的可积和超可积系统映射到不同流形上的其它系统.一般来说，CCM不保持运动常数的顺序，甚至不将动量多项式取为动量多项式。我们研究专业化的这些行动，保持多项式和结构的对称代数在经典和量子的情况下。我们给出了几个通过CCM得到的2维空间中的非常曲率3阶和4阶超可积系统的例子，并详细说明了变换作用所保持的对称代数的结构。
英文摘要：
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which do preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature 3rd and 4th order superintegrable systems in 2 space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
