Action中的多项式李代数$sl_{pd}(2)$：光滑$sl(2)$映射与逼近
Polynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations
摘要：
我们研究应用多项式李代数$sl_{pd}(2)$来解决量子物理中耦合子系统的$G_{inv}$不变模型中的物理任务。本文给出了一种求解谱问题的一般算子形式，它利用$sl_{pd}(2)$陪集生成元$V_{\pm}$中的广义相干态、本征函数和其它重要物理量的幂级数展开.我们还讨论了一些映射和近似熟悉的$sl(2)$代数形式主义。在这种方式下，一个新的封闭的解析表达式被发现的能量谱相吻合的精确解在某些情况下，并在一般情况下，体现了不可否认的本征频率有关的一个近混沌动力学系统的研究。
英文摘要：
We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using expansions of generalized coherent states, eigenfunctions and other physically important quantities by power series in the $sl_{pd}(2)$ coset generators $V_{\pm}$. We also discuss some mappings and approximations related to the familiar $sl(2)$ algebra formalism. On this way a new closed analytical expression is found for energy spectra which coincides with exact solutions in certain cases and, in general, manifests an availability of incommensurable eigenfrequencies related to a nearly chaotic dynamics of systems under study.
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