Projection on higher Landau levels and non-commutative geometry

TL;DR

This paper formulates the projection of a 2D system onto higher Landau levels using non-commutative geometry, resulting in a new class of star products that extend the mathematical framework of quantum Hall systems.

Contribution

It introduces a novel approach to describe higher Landau level projections through non-commutative geometry and defines new star products for this purpose.

Findings

Development of a new class of star products for higher Landau levels

Extension of non-commutative geometric methods to quantum Hall systems

Mathematical framework for analyzing projections in magnetic fields

Abstract

The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.