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 continuum. Taking inspiration from the ideas developed by Bellissard during the 80's, we build a spectral triple for the *-algebra of continuous magnetic operators based on a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211073 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects. Giuseppe De Nittis and Maximiliano Sandoval. SIGMA 16 (2020), 146, 50 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862599709557784576 |
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| author | De Nittis, Giuseppe Sandoval, Maximiliano |
| author_facet | De Nittis, Giuseppe Sandoval, Maximiliano |
| citation_txt | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects. Giuseppe De Nittis and Maximiliano Sandoval. SIGMA 16 (2020), 146, 50 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 *-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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| first_indexed | 2026-03-14T01:29:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211073 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T01:29:40Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | De Nittis, Giuseppe Sandoval, Maximiliano 2025-12-23T13:10:01Z 2020 The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects. Giuseppe De Nittis and Maximiliano Sandoval. SIGMA 16 (2020), 146, 50 pages 1815-0659 2020 Mathematics Subject Classification: 81R60; 58B34; 81R15; 81V70 arXiv:2006.06785 https://nasplib.isofts.kiev.ua/handle/123456789/211073 https://doi.org/10.3842/SIGMA.2020.146 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 *-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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects Article published earlier |
| spellingShingle | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects De Nittis, Giuseppe Sandoval, Maximiliano |
| title | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects |
| title_full | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects |
| title_fullStr | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects |
| title_full_unstemmed | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects |
| title_short | The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects |
| title_sort | noncommutative geometry of the landau hamiltonian: metric aspects |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211073 |
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