朗道哈密顿量的非交换几何:度量方面

arXiv: Mathematical Physics Pub Date : 2020-06-11 DOI:10.3842/sigma.2020.146

G. Nittis, M. Sandoval

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引用次数: 4

摘要

这项工作为连续空间中量子霍尔效应的非交换几何构造提供了第一步。从Bellissard在80年代发展的思想中获得灵感，我们基于具有紧解的Dirac算子，为连续磁算子的$C^*$-代数建立了一个谱三重。研究了这个谱三重体的度量方面，并证明了Bellissard理论的一个重要部分(所谓的第一Connes公式)。

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The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

This work provides a first step towards the construction of a noncommutative geometry for the Quantum Hall Effect in the continuous. 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.

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arXiv: Mathematical Physics

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