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Colección SciELO Chile

The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

Indexado

WoS	WOS:000607118600001
Scopus	SCOPUS_ID:85106168513

DOI

10.3842/SIGMA.2020.146

Año

2020

Tipo

artículo de investigación

Citas Totales

Autores Afiliación Chile

Instituciones Chile

% Participación
Internacional

Autores
Afiliación Extranjera

Instituciones
Extranjeras

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.

Revista

Revista	ISSN
Symmetry Integrability And Geometry Methods And Applications	1815-0659

Métricas Externas

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Disciplinas de Investigación

WOS
Mathematics
Physics, Mathematical

Scopus
Geometry And Topology
Analysis
Mathematical Physics

SciELO
Sin Disciplinas

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Publicaciones WoS (Ediciones: ISSHP, ISTP, AHCI, SSCI, SCI), Scopus, SciELO Chile.

Colaboración Institucional

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Autores - Afiliación

Ord.	Autor	Género	Institución - País
1	De Nittis, Giuseppe	Hombre	Pontificia Universidad Católica de Chile - Chile Facultad de Matemáticas - Chile
2	SANDOVAL-POZO, MAURICIO	Hombre	Pontificia Universidad Católica de Chile - Chile Facultad de Matemáticas - Chile

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Financiamiento

Fuente
CONICYT-PFCHA
Fondecyt Regular
Grant Fondecyt regular
grant CONICYT-PFCHA Doctorado Nacional
Fondecyt Regular-1190204
Hermann Schulz-Baldes

Muestra la fuente de financiamiento declarada en la publicación.

Agradecimientos

Agradecimiento
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. GD is indebted to Jean Bellissard, who is the real inspirer of this work. GD would like to cordially thank Chris Bourne, Massimo Moscolari, and Hermann Schulz-Baldes for several inspiring discussions. We would like to thank the anonymous referees for providing very useful suggestions which significantly improved the quality of this work.
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. GD is indebted to Jean Bellissard, who is the real inspirer of this work. GD would like to cordially thank Chris Bourne, Massimo Moscolari, and Hermann Schulz-Baldes for several inspiring discussions. We would like to thank the anonymous referees for providing very useful suggestions which significantly improved the quality of this work.

Agradecimiento

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. GD is indebted to Jean Bellissard, who is the real inspirer of this work. GD would like to cordially thank Chris Bourne, Massimo Moscolari, and Hermann Schulz-Baldes for several inspiring discussions. We would like to thank the anonymous referees for providing very useful suggestions which significantly improved the quality of this work.

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. GD is indebted to Jean Bellissard, who is the real inspirer of this work. GD would like to cordially thank Chris Bourne, Massimo Moscolari, and Hermann Schulz-Baldes for several inspiring discussions. We would like to thank the anonymous referees for providing very useful suggestions which significantly improved the quality of this work.