论文标题
量子SU的量子度量结构（2）
The quantum metric structure of quantum SU(2)
论文作者
论文摘要
我们在量子su（2）上引入了两个狄拉克运算符的参数家族，并从非交通性度量几何形状的角度分析了它们的性质。结果表明，这些狄拉克运算符会产生紧凑的量子度量结构，并且相应的两个紧凑型量子度量空间的参数家族在Rieffel的量子Gromov-Hausdorff距离中连续变化。这种连续性结果包括经典案例，我们将三轮赛季恢复到公制上的全局缩放系数。我们的主要技术工具是Berezin Transform的量子SU（2）及其相关的模糊近似值，其分析也导致了一种系统的方式，通过发电机中的多项式表达式近似Lipschitz运算符。
We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry. It is shown that these Dirac operators give rise to compact quantum metric structures, and that the corresponding two parameter family of compact quantum metric spaces varies continuously in Rieffel's quantum Gromov-Hausdorff distance. This continuity result includes the classical case where we recover the round 3-sphere up to a global scaling factor on the metric. Our main technical tool is a quantum SU(2) analogue of the Berezin transform, together with its associated fuzzy approximations, the analysis of which also leads to a systematic way of approximating Lipschitz operators by means of polynomial expressions in the generators.
