Coordinate noncommutativity in strong non-uniform magnetic fields

TL;DR

This paper investigates how spatial coordinates become noncommutative for a charged particle in strong, non-uniform magnetic fields, extending previous models and exploring implications in magnetic mirror configurations.

Contribution

It derives a generalized relation for coordinate commutators in non-uniform magnetic fields, expanding understanding beyond constant field cases.

Findings

Derived a generalized coordinate commutator relation for non-uniform magnetic fields

Analyzed noncommutativity effects in magnetic mirror configurations

Extended the theoretical framework of noncommutative geometry in magnetic systems

Abstract

Noncommuting spatial coordinates are studied in the context of a charged particle moving in a strong non-uniform magnetic field. We derive a relation involving the commutators of the coordinates, which generalizes the one realized in a strong constant magnetic field. As an application, we discuss the noncommutativity in the magnetic field present in a magnetic mirror.