双曲面上量子超可积系统的纠缠对称代数
Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid
摘要：
定义在二维双曲面上的一类量子超可积哈密顿量被认为是与一组交织算子连接它们。证明了这种交织算子封闭了一个su（2，1）李代数，并通过Casimir算子确定了Hamilton算子.利用离散对称性，得到了闭so（4，2）代数的更广泛的算子集.束缚态的离散谱所对应的物理态以及简并态用su（2，1）和so（4，2）的幺正表示来表征。
英文摘要：
A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra and determine the Hamiltonians through the Casimir operators. By means of discrete symmetries a broader set of operators is obtained closing a so(4,2) algebra. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of unitary representations of su(2,1) and so(4,2).
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