Quantum Hall Effect on the Hyperbolic Plane

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In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between $K$-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case.
AMS-LaTeX, 28 pages

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Differential Geometry, Functional Analysis, High Energy Physics - Theory, 58 (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/178571

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9704006
 http://arxiv.org/abs/dg-ga/9704006
 Commun.Math.Phys.190:629-673,1998
 doi:10.1007/s002200050255

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arXiv