Group theoretical construction of planar Noncommutative Phase Spaces

TL;DR

This paper constructs and classifies planar noncommutative phase spaces using group theoretical methods, revealing minimal couplings and providing physical interpretations of the generators involved.

Contribution

It introduces a novel group theoretical framework for constructing noncommutative phase spaces in planar systems, including both centrally and noncentrally extended Lie groups.

Findings

Coordinates do not commute due to natural fields.

Symplectic realizations yield physical interpretations.

Framework unifies different extensions of planar Lie groups.

Abstract

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.