The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
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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.
2007 ◽
pp. 235-261
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1994 ◽
Vol 35
(10)
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pp. 5373-5451
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1998 ◽
Vol 2
(1-4)
◽
pp. 523-526
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