论文标题
梯子操作员和隐藏代数，用于形状不变的非分离和非偏齿模型二次复杂相互作用。 ii。三维模型
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. II. Three-Dimensional Model
论文作者
论文摘要
Bardavelidze，Cannata，Ioffe和Nishnianidze引入了形状不可分化的非分离和非偏度的三维模型。但是，完整的隐藏对称代数和对约旦块形成的相关状态的描述仍有待研究。我们提出了一组六个运算符$ \ {a^{\ pm}，b^{\ pm}，c^{\ pm} \} $，可以组合以构建$ {\ mathfrak {gl}}}}（3）$。后者可以嵌入$ {\ mathfrak {sp}}（6）$代数，以及$ {\ mathfrak {osp}}}（1/6）$ superalgebra中。与特征态和制造约旦块相关的国家通过在基态上作用的操作员的组合以不同的方式诱导。我们介绍了这些操作员的作用，并研究了扩展生物三相基础的构建。这些依赖于建立各种非平凡多项式和换向因子身份。我们还在模型的隐藏对称性和基本的可共性属性之间建立了连接。有趣的是，积分产生一个立方代数。这项工作表明，如何广泛应用于隐性汉密尔顿人，例如隐藏的对称性，可鲁旋用和梯子操作员，并扩展到伪缓刑案例，并具有许多差异。
A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. However, the complete hidden symmetry algebra and the description of the associated states that form Jordan blocks remained to be studied. We present a set of six operators $\{A^{\pm},B^{\pm},C^{\pm}\}$ that can be combined to build a ${\mathfrak{gl}}(3)$ hidden algebra. The latter can be embedded in an ${\mathfrak{sp}}(6)$ algebra, as well as in an ${\mathfrak{osp}}(1/6)$ superalgebra. The states associated with the eigenstates and making Jordan blocks are induced in different ways by combinations of operators acting on the ground state. We present the action of these operators and study the construction of an extended biorthogonal basis. These rely on establishing various nontrivial polynomial and commutator identities. We also make a connection between the hidden symmetry and the underlying superintegrability property of the model. Interestingly, the integrals generate a cubic algebra. This work demonstrates how various concepts that have been applied widely to Hermitian Hamiltonians, such as hidden symmetries, superintegrability, and ladder operators, extend to the pseudo-Hermitian case with many differences.
