AG Mathematische Physik

THE NONCOMMUTATIVE GEOMETRY OF THE LANDAU
HAMILTONIAN: METRIC ASPECTS

Maximiliano Sandoval, Santiago, Chile

Abstract: This work provides a first step towards the construction
of a noncommutative geometry for the Quantum Hall Effect in the
continuous. 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.