Classical mechanics in noncommutative spaces: confinement and more

Author(s)

Kupriyanov, Vladislav ; Kurkov, Maxim ; Sharapov, Alexey

• Document type: Journal article
• Source: EUROPEAN PHYSICAL JOURNAL C; v. 84, n. 10, p. 13-pg., 2024-10-16.

Abstract

We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the corresponding phase space is given by the cotangent bundle of a Lie group, with the Lie group playing the role of a curved momentum space. We show that the curvature of the momentum space may lead to rather unexpected physical phenomena such as an upper bound on the velocity of a free nonrelativistic particle, bounded motion for repulsive central force, and no-fall-into-the-centre for attractive Coulomb potential. We also consider a superintegrable Hamiltonian for the Kepler problem in 3-space with su(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {su}(2)$$\end{document} noncommutativity. The leading correction to the equations of motion due to noncommutativity is shown to be described by an effective monopole potential. (AU)

• FAPESP's process: 24/04134-6 - Poisson Electrodynamics and Applications
• Grantee: Vladislav Kupriyanov
• Support Opportunities: Regular Research Grants