The main aim of this work is to build unitary phase operators and the corresponding temporally stable phase states for the [Formula: see text] Lie algebra. We first introduce an irreducible finite-dimensional Hilbertian representation of the [Formula: see text] Lie algebra which is suitable for our purpose. The phase operators obtained from the [Formula: see text] generators are defined and the phase states are derived as eigenstates associated to these unitary phase operators. The special cases of [Formula: see text] and [Formula: see text] Lie algebras are also explicitly investigated.

中文翻译：

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与 su(n + 1) 李代数相关的相位算子和相位状态

这项工作的主要目的是为[公式：见文本]李代数建立酉相位算子和相应的时间稳定相位状态。我们首先介绍适合我们目的的[公式：见文本]李代数的不可约有限维希尔伯特表示。从[公式：见文本]生成器获得的相位算子被定义，并且相位状态被导出为与这些单一相位算子相关的本征态。[公式：见正文]和[公式：见正文]李代数的特殊情况也被明确研究。