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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 146, 50 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.146 (Mi sigma1682) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

Giuseppe De Nittisab, Maximiliano Sandovala

a Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile
b Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
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DOI: https://doi.org/10.3842/SIGMA.2020.146
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.
Keywords: Landau Hamiltonian, spectral triple, Dixmier trace, first Connes' formula.
Funding agency Grant number
Fondo Nacional de Desarrollo Científico y Tecnológico 1190204
Comisión Nacional de Investigación Científica y Tecnológica 2018-21181868
GD's research is supported by the grant Fondecyt Regular - 1190204. MS's research is supported by the grant CONICYT-PFCHA Doctorado Nacional 2018-21181868.
Received: June 12, 2020; in final form December 22, 2020; Published online December 28, 2020
Bibliographic databases:
Document Type: Article
MSC: 81R60, 58B34, 81R15, 81V70
Language: English
Citation: Giuseppe De Nittis, Maximiliano Sandoval, “The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects”, SIGMA, 16 (2020), 146, 50 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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