Noncommutative Phase Spaces by Coadjoint Orbits Method

TL;DR

This paper constructs noncommutative phase spaces using coadjoint orbits of anisotropic Newton-Hooke groups, illustrating how magnetic and dual magnetic fields induce noncommutativity in positions and momenta.

Contribution

It introduces a novel method of realizing noncommutative phase spaces via coadjoint orbits of specific Lie groups, expanding the geometric understanding of noncommutativity.

Findings

Realization of noncommutative phase spaces as coadjoint orbits.

Demonstration of noncommutativity induced by magnetic fields.

Extension to two- and three-dimensional spaces.

Abstract

We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.