Classical mechanics in noncommutative spaces: confinement and more
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...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-10-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-13372-7 |
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| author | Vladislav Kupriyanov Maxim Kurkov Alexey Sharapov |
| author_facet | Vladislav Kupriyanov Maxim Kurkov Alexey Sharapov |
| author_sort | Vladislav Kupriyanov |
| collection | DOAJ |
| description | 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 $$\mathfrak {su}(2)$$ 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 | Article |
| id | doaj-art-05b46013a5314c9583375f2fe3e9fdcd |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-05b46013a5314c9583375f2fe3e9fdcd2024-12-08T12:43:02ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-10-01841011310.1140/epjc/s10052-024-13372-7Classical mechanics in noncommutative spaces: confinement and moreVladislav Kupriyanov0Maxim Kurkov1Alexey Sharapov2Centro de Matemática, Computação e Cognição, Universidade Federal do ABCDipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6Physics Faculty, Tomsk State UniversityAbstract 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 $$\mathfrak {su}(2)$$ su ( 2 ) noncommutativity. The leading correction to the equations of motion due to noncommutativity is shown to be described by an effective monopole potential.https://doi.org/10.1140/epjc/s10052-024-13372-7 |
| spellingShingle | Vladislav Kupriyanov Maxim Kurkov Alexey Sharapov Classical mechanics in noncommutative spaces: confinement and more European Physical Journal C: Particles and Fields |
| title | Classical mechanics in noncommutative spaces: confinement and more |
| title_full | Classical mechanics in noncommutative spaces: confinement and more |
| title_fullStr | Classical mechanics in noncommutative spaces: confinement and more |
| title_full_unstemmed | Classical mechanics in noncommutative spaces: confinement and more |
| title_short | Classical mechanics in noncommutative spaces: confinement and more |
| title_sort | classical mechanics in noncommutative spaces confinement and more |
| url | https://doi.org/10.1140/epjc/s10052-024-13372-7 |
| work_keys_str_mv | AT vladislavkupriyanov classicalmechanicsinnoncommutativespacesconfinementandmore AT maximkurkov classicalmechanicsinnoncommutativespacesconfinementandmore AT alexeysharapov classicalmechanicsinnoncommutativespacesconfinementandmore |