A Stochastic Origin of Spacetime Non-Commutativity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910868755709952 |
|---|---|
| author | Arzano, Michele Kuipers, Folkert |
| author_facet | Arzano, Michele Kuipers, Folkert |
| contents | We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $κ$-Minkowski spacetime commutators can be obtained. Moreover we focus on modifications of the Leibniz rule for differentials acting on discontinuous trajectories. We show how these can be related to the deformed action of translation generators focusing, as a working example, on the $κ$-Poincaré algebra. Our findings suggest that spacetime non-commutativity can be understood as a result of fundamental discreteness in temporal and/or spatial evolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Stochastic Origin of Spacetime Non-Commutativity Arzano, Michele Kuipers, Folkert High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $κ$-Minkowski spacetime commutators can be obtained. Moreover we focus on modifications of the Leibniz rule for differentials acting on discontinuous trajectories. We show how these can be related to the deformed action of translation generators focusing, as a working example, on the $κ$-Poincaré algebra. Our findings suggest that spacetime non-commutativity can be understood as a result of fundamental discreteness in temporal and/or spatial evolution. |
| title | A Stochastic Origin of Spacetime Non-Commutativity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.11866 |