Classical Mechanics in Noncommutative Spaces: Confinement and More
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2024
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| _version_ | 1866911884573147136 |
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| author | Kupriyanov, Vladislav Kurkov, Maxim Sharapov, Alexey |
| author_facet | Kupriyanov, Vladislav Kurkov, Maxim Sharapov, Alexey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical Mechanics in Noncommutative Spaces: Confinement and More Kupriyanov, Vladislav Kurkov, Maxim Sharapov, Alexey High Energy Physics - Theory Mathematical Physics 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. |
| title | Classical Mechanics in Noncommutative Spaces: Confinement and More |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2405.09348 |