Magnetic Backgrounds from Generalised Complex Manifolds

TL;DR

This paper demonstrates that generalised complex manifolds can geometrically generate magnetic backgrounds, providing a new perspective on spacetime noncommutativity and rederiving Landau model Poisson brackets.

Contribution

It introduces a novel geometric approach using generalised complex manifolds to model magnetic backgrounds, expanding the tools beyond noncommutative geometry.

Findings

Generalised complex manifolds can produce B-fields geometrically.

Rederived Landau model Poisson brackets using this approach.

Provides a new geometric framework for magnetic backgrounds.

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.