论文标题
融合多项式代数的新的玻色子实现在非铁量量子力学中：$γ$ -deformed $ su（2）$发电机，部分$ \ MATHCAL {pt} $ - 对称性和Higgs algebra
A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $γ$-deformed $su(2)$ generators, Partial $\mathcal{PT}$-symmetry and Higgs algebra
论文作者
论文摘要
从$ \ bf {c^2} $中获得了$ su（2）$代数的$ SU（2）$代数的$γ$（2）$代数的版本。相关的Jordan-Schwinger（J-S）图与玻色子代数相结合，以获得融合多项式代数的层次结构。这使得立方多项式类型的希格斯代数的构建可能。最后，已引入了部分$ \ Mathcal {pt} $对称性的概念，作为某些操作员及其特征功能的特征特征。还讨论了部分$ \ MATHCAL {PT} $ - 对称破坏的可能性。变形参数$γ$在整个配方中起着至关重要的作用，非琐事修改了所考虑的本征函数。
A $γ$-deformed version of $su(2)$ algebra with non-hermitian generators has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. The related Jordan-Schwinger(J-S) map is combined with boson algebras to obtain a hierarchy of fusion polynomial algebras. This makes possible the construction of Higgs algebra of cubic polynomial type. Finally the notion of partial $\mathcal{PT}$ symmetry has been introduced as characteristic feature of some operators as well as their eigenfunctions. The possibility of partial $\mathcal{PT}$-symmetry breaking is also discussed. The deformation parameter $γ$ plays a crucial role in the entire formulation and non-trivially modifies the eigenfunctions under consideration.
