The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

Symmetry Integrability and Geometry-Methods and Applications

article

Giuseppe De Nittis¹  Maximiliano Sandoval¹ 

[1] Facultad de Matemáticas & Instituto de Física, Pontificia Universidad Católica de Chile

关键词: Landau Hamiltonian;    spectral triple;    Dixmier trace;    first Connes’ formula 2020 Mathematics Subject Classification 81R60;    58B34;    81R15;    81V70;   

DOI  :  10.3842/SIGMA.2020.146

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown