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arXiv · 2006.06785

The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

Giuseppe De Nittis·Maximiliano Sandoval
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Abstract

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.

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Giuseppe De Nittis, Maximiliano Sandoval. 2020-06-11. The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects. https://doi.org/10.3842/sigma.2020.146

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