Advances in Theoretical and Mathematical Physics

Volume 16 (2012)

Number 2

Generalized TKNN-equations

Pages: 505 – 547



Giovanni Landi (Dipartimento di Matematica, Università di Trieste, Italy; INFN, Sezione di Trieste, Italy)

Giuseppe de Nittis (LAGA, Institut Galilée, Université Paris, Villetaneuse, France)


We derive generalized TKNN-equations via bundle representations of the noncommutative torus with rational deformation parameter, the bundle coming from spectral projections in the torus algebra. These equations relate Chern numbers of dual bundles, which we interpret as Hall conductances for Dirac-like Hamiltonians describing magnetic Bloch electrons in a strong magnetic field. We also present their generalizations for irrational values of the deformation parameter.

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