The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• ISSN: 1815-0659
• Main Authors: De Nittis, Giuseppe, Sandoval, Maximiliano
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211073
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects. Giuseppe De Nittis and Maximiliano Sandoval. SIGMA 16 (2020), 146, 50 pages

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...