In this paper, we introduce an SU(1, 1) algebraic approach to study the (2 + 1)-Dirac oscillator in the presence of the Aharonov–Casher effect coupled to an external electromagnetic field in the Minkowski spacetime and the cosmic string spacetime. This approach is based on a quantum mechanics factorization method that allows us to obtain the su(1, 1) algebra generators, the energy spectrum and the eigenfunctions. We obtain the coherent states and their temporal evolution for each spinor component of this problem. Finally, for these problems, we calculate some matrix elements and the Schrödinger uncertainty relationship for two general SU(1, 1) operators.

中文翻译：

---

宇宙弦背景中狄拉克振子与 Aharonov-Casher 系统相互作用的代数解和相干态

在本文中，我们介绍了一种 SU(1, 1) 代数方法来研究在存在与 Minkowski 时空和宇宙弦时空中的外部电磁场耦合的 Aharonov-Casher 效应的情况下的 (2 + 1)-Dirac 振子. 这种方法基于量子力学分解方法，该方法允许我们获得 su(1, 1) 代数发生器、能谱和特征函数。我们获得了该问题的每个旋量分量的相干状态及其时间演化。最后，针对这些问题，我们计算了两个通用 SU(1, 1) 算子的一些矩阵元素和薛定谔不确定性关系。