2024/05/15 by Vladislav Kupriyanov, Kupriyanov, Vladislav, Maxim Kurkov +3 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2405.09348
openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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) noncommutativity. The leading correction to the equations of motion due to noncommutativity is shown to be described by an effective monopole potential.