非线性角动量代数的非齐次玻色子实现

Inhomogeneous Boson realizations of nonlinear angular momentum algebra

在量子系统的非线性对称性的研究领域中 ,利用Poincaré- Birkhoff- Witt理论 ,得到了非线性角动量代数 IΩ(Ω 为多项式的最高次幂 )在其通用包络代数空间上的不可分表示及在两个商空间上的诱导表示 ,并在此基础上具体给出了 IΩ 的非齐次的单、双和三玻色子实现。这些结果有助于对量子系统中非线性对称性的研究 ,进而加深对该系统的基本物理性质的理解。

In the nonlinear symmetries of quantum systems, explicit expressions were obtained for the indecomposable representation of the nonlinear angular momentum algebra I Ω on the space of its universal enveloping algebra and for two induced representations on the corresponding quotient spaces using Poincaré Birkhoff Witt theory. These expressions were used to derive the inhomogeneous single , double and triple Boson realizations of I Ω. These results can be used to study nonlinear symmetries in quantum systems and the basic physical properties of these systems.