Magnetic Backgrounds from Generalised Complex Manifolds

Abstract

The magnetic backgrounds that physically give rise to spacetime noncommutativity are generally treated using noncommutative geometry. In this article we prove that also the theory of generalised complex manifolds contains the necessary elements to generate B-fields geometrically. As an example, the Poisson brackets of the Landau model (electric charges on a plane subject to an external, perperdicularly applied magnetic field) are rederived using the techniques of generalised complex manifolds.