论文标题
物质重模耦合，用于模糊几何和Landau-Hall问题
Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem
论文作者
论文摘要
我们考虑一组物理自由度与有限维的希尔伯特空间相结合，可以将其作为模拟空间建模，也可以作为Landau-hall问题的最低兰道水平。这些可能被视为模糊空间上的物质字段。我们认为有效的作用是由与狄拉克指数密度相关的Chern-Simons形式（具有仪表和重力场）相关的，有效的作用是由Chern-simons形式给出的，而庞加尔 - 卡丹形式的ABELIAN仪表场则以物质动力学的形式转移。结果是对物质场的作用，其中拉格朗日与曲线中特定多项式的密度集成在一起。
We consider a set of physical degrees of freedom coupled to a finite-dimensional Hilbert space, which may be taken as modeling a fuzzy space or as the lowest Landau level of a Landau-Hall problem. These may be viewed as matter fields on a fuzzy space. Sequentially generalizing to arbitrary backgrounds, we argue that the effective action is given by the Chern-Simons form associated with the Dirac index density (with gauge and gravitational fields), with an abelian gauge field shifted by the Poincaré-Cartan form for matter dynamics. The result is an action for matter fields where the Lagrangian is integrated with a density which is a specific polynomial in the curvatures.
