Magnetic Schro¨dinger Operator from the Point of View of Noncommutative Geometry


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Abstract

We give an interpretation of magnetic Schro¨dinger operator in terms of noncommutative geometry. In particular, spectral properties of this operator are reformulated in terms of C∗-algebras. Using this reformulation, one can employ the machinery of noncommutative geometry, such as Hochschild cohomology, to study the properties of magnetic Schro¨dinger operator. We show how this idea can be applied to the integer quantum Hall e ect.

About the authors

A. G. Sergeev

Steklov Mathematical Institute

Email: sergeev@mi.ras.ru
Moscow, Russia

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