论文标题
超级量子力学中的超级综合性和双$ -1 $ -1 $ hahn代数
Superintegrability and the dual $-1$ Hahn algebra in superconformal quantum mechanics
论文作者
论文摘要
确定并精确地解决了具有内部自由度的奇异振荡器的二维可整合系统。它的对称代数被认为是双$ -1 $ hahn代数，它描述了多项式的双光谱属性，其名称本质上是SuperConformal Elgebra $ \ Mathfrak {osp}（osp}（osp}（1 | 2）$的Clebsch-Gordan系数。还显示了如何从四个维度中的一组未耦合的谐波振荡器的尺寸降低下获得这种可整合的模型。
A two-dimensional superintegrable system of singular oscillators with internal degrees of freedom is identified and exactly solved. Its symmetry algebra is seen to be the dual $-1$ Hahn algebra which describes the bispectral properties of the polynomials with the same name that are essentially the Clebsch-Gordan coefficients of the superconformal algebra $\mathfrak{osp}(1|2)$. It is also shown how this superintegrable model is obtained under dimensional reduction from a set of uncoupled harmonic oscillators in four dimensions.
