论文标题
Landau Hamiltonian的非交通性几何形状：度量方面
The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
论文作者
论文摘要
这项工作为连续体的量子厅效应构建非交通性几何形状提供了第一步。从贝里萨德（Bellissard）在80年代开发的想法中汲取灵感，我们基于具有紧凑型分辨率的狄拉克操作员的$ c^*$ - 连续磁性操作员的代数。研究了该频谱三重的度量方面，并证明了贝里萨德（Bellissard）理论的重要一部分（所谓的第一条康纳斯公式）。
This work provides a first step towards the construction of a noncommutative geometry for the quantum Hall effect in the continuum. Taking inspiration from the ideas developed by Bellissard during the 80's we build a spectral triple for the $C^*$-algebra of continuous magnetic operators based on a Dirac operator with compact resolvent. The metric aspects of this spectral triple are studied, and an important piece of Bellissard's theory (the so-called first Connes' formula) is proved.
