Para-Galilean versus Galilean Noncommutative Phase spaces

TL;DR

This paper constructs noncommutative phase spaces from group theory, revealing how dual magnetic fields induce noncommutativity in Galilei and Para-Galilei groups in two dimensions.

Contribution

It introduces a novel geometric approach to noncommutative phase spaces using coadjoint orbits of extended Galilei and Para-Galilei groups.

Findings

Noncommutative phase spaces are modeled as coadjoint orbits.

Dual magnetic fields B* and B induce noncommutativity.

The construction differs between Galilei and Para-Galilei cases.

Abstract

The present paper deals with the construction of noncommutative phase spaces as coadjoint orbits of noncentral extensions of Galilei and Para-Galilei groups in two-dimensional space. The noncommutativity is due to the presence of a dual magnetic field B* in the Galilei case and of a magnetic field B in the Para-Galilei case.