论文标题
$（5）$ landau型号和嵌套的nambu矩阵几何形状
$SO(5)$ Landau Models and Nested Nambu Matrix Geometry
论文作者
论文摘要
$ SO（5）$ LANDAU模型是4D量子厅效应的数学平台，为实现模糊四个球的物理实现提供了难得的机会。我们对$（5）$ landau模型和通过Landau级别投影的相关矩阵几何形状进行了综合分析。 With the $SO(5)$ monopole harmonics, we explicitly derive matrix geometry of a four-sphere in any Landau level: In the lowest Landau level the matrix coordinates are given by the generalized $SO(5)$ gamma matrices of the fuzzy four-sphere satisfying the quantum Nambu algebra, while in higher Landau levels the matrix geometry becomes a nested模糊的结构实现了纯量子几何形状，而在古典几何形状中没有对应物。在$（4）$ Pauli-Schrödinger模型和$ SO（4）$ Landau模型的视图中，讨论了内部模糊几何结构，我们在其背景非亚洲字段配置之间揭开了隐藏的奇异仪表转换。还研究了$（5）$ landau模型的相对论版本，并阐明了与Berezin-Toeplitz量化的关系。我们最终在更高的维度上讨论了Landau模型的矩阵几何形状。
The $SO(5)$ Landau model is the mathematical platform of the 4D quantum Hall effect and provide a rare opportunity for a physical realization of the fuzzy four-sphere. We present an integrated analysis of the $SO(5)$ Landau models and the associated matrix geometries through the Landau level projection. With the $SO(5)$ monopole harmonics, we explicitly derive matrix geometry of a four-sphere in any Landau level: In the lowest Landau level the matrix coordinates are given by the generalized $SO(5)$ gamma matrices of the fuzzy four-sphere satisfying the quantum Nambu algebra, while in higher Landau levels the matrix geometry becomes a nested fuzzy structure realizing a pure quantum geometry with no counterpart in classical geometry. The internal fuzzy geometry structure is discussed in the view of an $SO(4)$ Pauli-Schrödinger model and the $SO(4)$ Landau model, where we unveil a hidden singular gauge transformation between their background non-Abelian field configurations. Relativistic versions of the $SO(5)$ Landau model are also investigated and relationship to the Berezin-Toeplitz quantization is clarified. We finally discuss the matrix geometry of the Landau models in even higher dimensions.
