N维弯曲空间上的超可积性：中心势、离心项和磁单极
Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
摘要：
由一个弯曲的动力学项（取决于函数f）、一个中心势（取决于函数U）、一个狄拉克项和N个离心项构成的N维哈密顿量H对于函数f和U的任何选择都是准极大超可积的。利用H的sl（2，R）-余代数对称性证明了这一结果，从而得到了一组（2N-3）函数独立的运动积分。这样的运动常数是“普适的”，因为它们都与f和U无关。这个哈密顿量描述了粒子在任意中心势U作用下在任意ND球对称弯曲空间（其度规由函数f指定）上的运动，并且同时包括一个抛物型贡献以及N个打破球对称的离心项。此外，我们表明，两个适当的选择U提供的“本征”振荡器和KC潜力，这些弯曲的流形。作为一个副产品，MIC-Kepler，Taub-NUT和所谓的多重开普勒系统被证明属于这类超可积哈密顿量，并得到新的推广。讨论了四个达布曲面的N维推广的开普勒势和振子势。
英文摘要：
The N-dimensional Hamiltonian H formed by a curved kinetic term (depending on a function f), a central potential (depending on a function U), a Dirac monopole term, and N centrifugal terms is shown to be quasi-maximally superintegrable for any choice of the functions f and U. This result is proven by making use of the underlying sl(2,R)-coalgebra symmetry of H in order to obtain a set of (2N-3) functionally independent integrals of the motion, that are explicitly given. Such constants of the motion are "universal" since all of them are independent of both f and U. This Hamiltonian describes the motion of a particle on any ND spherically symmetric curved space (whose metric is specified by a function f) under the action of an arbitrary central potental U, and includes simultaneously a monopole-type contribution together with N centrifugal terms that break the spherical symmetry. Moreover, we show that two appropriate choices for U provide the "intrinsic" oscillator and the KC potentials on these curved manifolds. As a byproduct, the MIC-Kepler, the Taub-NUT and the so called multifold Kepler systems are shown to belong to this class of superintegrable Hamiltonians, and new generalizations thereof are obtained. The Kepler and oscillator potentials on N-dimensional generalizations of the four Darboux surfaces are discussed as well.
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