We study the algebraic structure of the one-dimensional Dirac oscillator by extending the concept of spin symmetry to a noncommutative case. An SO(4) algebra is found connecting the eigenstates of the Dirac oscillator, in which the two elements of Cartan subalgebra are conserved quantities. Similar results are obtained in the Jaynes--Cummings model.

中文翻译：

---

1+1 Dirac Oscillator 和 Jaynes-Cummings 模型中的动力学代数

我们通过将自旋对称的概念扩展到非对易情况来研究一维狄拉克振荡器的代数结构。发现连接狄拉克振子的本征态的 SO(4) 代数，其中嘉当子代数的两个元素是守恒量。在 Jaynes--Cummings 模型中获得了类似的结果。