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。 I.二维模型
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
论文作者
论文摘要
由Cannata，Ioffe和Nishnianidze首先研究的形状不可分割的，不可分离的二维模型，具有二维相互作用，其目的是表现出其隐藏的代数结构。 The two operators $A^+$ and $A^-$, coming from the shape invariant supersymmetrical approach, where $A^+$ acts as a raising operator while $A^-$ annihilates all wavefunctions, are completed by introducing a novel pair of operators $B^+$ and $B^-$, where $B^-$ acts as the missing lowering operator.然后，这四个操作员充当构建$ {\ mathfrak {gl}}}（2）$发电机的构建块，作用在与给定能量特征值相对应的Jordan Block的一组关联功能中。该分析通过构建两对玻体操作员，最终产生了$ {\ mathfrak {sp}}}（4）$ algebra，以及$ {\ mathfrak {osp}}（1/4）$ superalgebra。因此，模型的隐藏代数结构与二维实际谐波振荡器所知的代数结构非常相似。
A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of exhibiting its hidden algebraic structure. The two operators $A^+$ and $A^-$, coming from the shape invariant supersymmetrical approach, where $A^+$ acts as a raising operator while $A^-$ annihilates all wavefunctions, are completed by introducing a novel pair of operators $B^+$ and $B^-$, where $B^-$ acts as the missing lowering operator. These four operators then serve as building blocks for constructing ${\mathfrak{gl}}(2)$ generators, acting within the set of associated functions belonging to the Jordan block corresponding to a given energy eigenvalue. This analysis is extended to the set of Jordan blocks by constructing two pairs of bosonic operators, finally yielding an ${\mathfrak{sp}}(4)$ algebra, as well as an ${\mathfrak{osp}}(1/4)$ superalgebra. Hence, the hidden algebraic structure of the model is very similar to that known for the two-dimensional real harmonic oscillator.
