标题： 手性与非交换球面上的狄拉克算子 显示英文标题

标题： Chirality and Dirac Operator on Noncommutative Sphere

摘要： 我们给出了在玻色子模糊球面框架下非交换$2$-球面上狄拉克算子的推导，并定义了康奈斯三元组。 结果表明，狄拉克算子存在两种不同的谱，相应地存在两类量子化代数。 作为结果，我们在贝雷津量子化中得到了对普朗克常数的新限制。 非交换几何中的局部框架映射也进行了讨论。 显示英文摘要

摘要： We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and correspondingly there are two classes of quantized algebras. As a result we obtain a new restriction on the Planck constant in Berezin's quantization. The map to the local frame in noncommutative geometry is also discussed.