A Novel Approach to Noncommutativity in Planar Quantum Mechanics

TL;DR

This paper explores how noncommutative algebra naturally arises in planar quantum mechanics, linking dissipation, dual descriptions of magnetic systems, and fluid dynamics, revealing new insights into quantum noncommutativity.

Contribution

It demonstrates that noncommutative structures in planar quantum mechanics can be derived from 't Hooft's dissipation analysis, unifying different physical models under a common framework.

Findings

Noncommutativity in coordinates and momenta are dual descriptions.

Dissipation analysis leads to noncommutative algebra in quantum systems.

Fluid dynamical models exhibit noncommutative features analogous to Landau levels.

Abstract

Noncommutative algebra in planar quantum mechanics is shown to follow from 't Hooft's recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a charged particle in a magnetic field with an oscillator potential are shown as dual descriptions of the same phenomenon. Finally, noncommutativity in a fluid dynamical model, analogous to the lowest Landau level problem, is discussed.