Symplectic Groupoids and Poisson Electrodynamics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910334398234624 |
|---|---|
| author | Kupriyanov, Vladislav G. Sharapov, Alexey A. Szabo, Richard J. |
| author_facet | Kupriyanov, Vladislav G. Sharapov, Alexey A. Szabo, Richard J. |
| contents | We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we interpret as the classical phase space of a point particle on noncommutative spacetime. In this picture gauge fields arise as bisections of the symplectic groupoid while gauge transformations are parameterized by Lagrangian bisections. We provide a geometric construction of a gauge invariant action functional which minimally couples a dynamical charged particle to a background electromagnetic field. Our constructions are elucidated by several explicit examples, demonstrating the appearances of curved and even compact momentum spaces, the interplay between gauge transformations and spacetime diffeomorphisms, as well as emergent gravity phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07406 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symplectic Groupoids and Poisson Electrodynamics Kupriyanov, Vladislav G. Sharapov, Alexey A. Szabo, Richard J. High Energy Physics - Theory Mathematical Physics Quantum Algebra Symplectic Geometry We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we interpret as the classical phase space of a point particle on noncommutative spacetime. In this picture gauge fields arise as bisections of the symplectic groupoid while gauge transformations are parameterized by Lagrangian bisections. We provide a geometric construction of a gauge invariant action functional which minimally couples a dynamical charged particle to a background electromagnetic field. Our constructions are elucidated by several explicit examples, demonstrating the appearances of curved and even compact momentum spaces, the interplay between gauge transformations and spacetime diffeomorphisms, as well as emergent gravity phenomena. |
| title | Symplectic Groupoids and Poisson Electrodynamics |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2308.07406 |