论文标题
量子矩阵几何形状在最低的Landau水平和更高的Landau级别
Quantum matrix geometry in the lowest Landau level and higher Landau levels
论文作者
论文摘要
Madore教授最著名的作品之一是引入模糊领域。我简要回顾了如何在非亚伯利亚单子背景的（球形）Landau模型中实现模糊的两个球及其更高维度的表亲。为了从Landau模型中提取量子几何形状，我们评估了最低和较高的Landau水平的球体坐标的矩阵元素。对于最低的Landau水平，矩阵几何形状被鉴定为模糊球的几何形状。同时，对于较高的Landau水平，获得的量子几何形状被证明是没有经典对应物的嵌套基质几何形状。模糊几何形状与不同维度中的单极管之间存在分层结构。维度层次结构表示量子异常尺寸梯子的Landau模型对应物。
One of the most celebrated works of Professor Madore is the introduction of fuzzy sphere. I briefly review how the fuzzy two-sphere and its higher dimensional cousins are realized in the (spherical) Landau models in non-Abelian monopole backgrounds. For extracting quantum geometry from the Landau models, we evaluate the matrix elements of the coordinates of spheres in the lowest and higher Landau levels. For the lowest Landau level, the matrix geometry is identified as the geometry of fuzzy sphere. Meanwhile for the higher Landau levels, the obtained quantum geometry turns out to be a nested matrix geometry with no classical counterpart. There exists a hierarchical structure between the fuzzy geometries and the monopoles in different dimensions. That dimensional hierarchy signifies a Landau model counterpart of the dimensional ladder of quantum anomaly.
