Noncommutative spaces of worldlines
The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincaré group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson homogeneous structure compatible with a given Poisson-Lie Poincaré gr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2019-05-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269319301868 |
| _version_ | 1818613669450219520 |
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| author | Angel Ballesteros Ivan Gutierrez-Sagredo Francisco J. Herranz |
| author_facet | Angel Ballesteros Ivan Gutierrez-Sagredo Francisco J. Herranz |
| author_sort | Angel Ballesteros |
| collection | DOAJ |
| description | The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincaré group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson homogeneous structure compatible with a given Poisson-Lie Poincaré group, the quantization of this Poisson bracket gives rise to a noncommutative space of worldlines with quantum group invariance. As an oustanding example, the Poisson homogeneous space of worldlines coming from the κ-Poincaré deformation is explicitly constructed, and shown to define a symplectic structure on the space of worldlines. Therefore, the quantum space of κ-Poincaré worldlines is just the direct product of three Heisenberg-Weyl algebras in which the parameter κ−1 plays the very same role as the Planck constant ħ in quantum mechanics. In this way, noncommutative spaces of worldlines are shown to provide a new suitable and fully explicit arena for the description of quantum observers with quantum group symmetry. Keywords: Time-like worldlines, Quantum groups, Poisson homogeneous spaces, Kappa-deformation, Non-commutative spaces, Quantum observers |
| first_indexed | 2024-12-16T16:05:47Z |
| format | Article |
| id | doaj.art-caa164adc8f0486fa8013e8e5b3d7cf6 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-12-16T16:05:47Z |
| publishDate | 2019-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-caa164adc8f0486fa8013e8e5b3d7cf62022-12-21T22:25:22ZengElsevierPhysics Letters B0370-26932019-05-01792175181Noncommutative spaces of worldlinesAngel Ballesteros0Ivan Gutierrez-Sagredo1Francisco J. Herranz2Corresponding author.; Departamento de Física, Universidad de Burgos, 09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, 09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, 09001 Burgos, SpainThe space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincaré group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson homogeneous structure compatible with a given Poisson-Lie Poincaré group, the quantization of this Poisson bracket gives rise to a noncommutative space of worldlines with quantum group invariance. As an oustanding example, the Poisson homogeneous space of worldlines coming from the κ-Poincaré deformation is explicitly constructed, and shown to define a symplectic structure on the space of worldlines. Therefore, the quantum space of κ-Poincaré worldlines is just the direct product of three Heisenberg-Weyl algebras in which the parameter κ−1 plays the very same role as the Planck constant ħ in quantum mechanics. In this way, noncommutative spaces of worldlines are shown to provide a new suitable and fully explicit arena for the description of quantum observers with quantum group symmetry. Keywords: Time-like worldlines, Quantum groups, Poisson homogeneous spaces, Kappa-deformation, Non-commutative spaces, Quantum observershttp://www.sciencedirect.com/science/article/pii/S0370269319301868 |
| spellingShingle | Angel Ballesteros Ivan Gutierrez-Sagredo Francisco J. Herranz Noncommutative spaces of worldlines Physics Letters B |
| title | Noncommutative spaces of worldlines |
| title_full | Noncommutative spaces of worldlines |
| title_fullStr | Noncommutative spaces of worldlines |
| title_full_unstemmed | Noncommutative spaces of worldlines |
| title_short | Noncommutative spaces of worldlines |
| title_sort | noncommutative spaces of worldlines |
| url | http://www.sciencedirect.com/science/article/pii/S0370269319301868 |
| work_keys_str_mv | AT angelballesteros noncommutativespacesofworldlines AT ivangutierrezsagredo noncommutativespacesofworldlines AT franciscojherranz noncommutativespacesofworldlines |