Quantum Hall Effect on the Hyperbolic Plane

Details Quantum Hall Effect on the Hyperbolic Plane Quantum Hall Effect on the Hyperbolic Plane

1997-04-10

arxiv.org/abs/dg-ga/9704006v1

Commun.Math.Phys.190:629-673,1998

Physics

High Energy Physics

High Energy Physics - Theory

AMS-LaTeX, 28 pages

Scientific paper

10.1007/s002200050255

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.

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