Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911226064273408 |
|---|---|
| author | Wallet, Jean-Christophe |
| author_facet | Wallet, Jean-Christophe |
| contents | The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based differential calculus possibly twisted and noncommutative analog of the Koszul connection. The star-products related to the quantum space-times are obtained from a combination of harmonic analysis of group algebras combined with Weyl quantization. The remaining problems inherent to gauge theories on Moyal spaces in their two different formulations are outlined. A family of gauge invariant matrix models on $\mathbb{R}^3_λ$, a deformation of $\mathbb{R}^3$ is presented among which a solvable model. The characterization of 11 new quantum Minkowski space-times through their $*$-algebras is given. A gauge theory of Yang-Mills type is constructed on one recently explored of these space-times and compared to its counterpart built on the popular $κ$-Minkowski. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview Wallet, Jean-Christophe High Energy Physics - Theory Mathematical Physics 81T75, 81T13, 81T32, 46L87, 17B37 The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based differential calculus possibly twisted and noncommutative analog of the Koszul connection. The star-products related to the quantum space-times are obtained from a combination of harmonic analysis of group algebras combined with Weyl quantization. The remaining problems inherent to gauge theories on Moyal spaces in their two different formulations are outlined. A family of gauge invariant matrix models on $\mathbb{R}^3_λ$, a deformation of $\mathbb{R}^3$ is presented among which a solvable model. The characterization of 11 new quantum Minkowski space-times through their $*$-algebras is given. A gauge theory of Yang-Mills type is constructed on one recently explored of these space-times and compared to its counterpart built on the popular $κ$-Minkowski. |
| title | Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview |
| topic | High Energy Physics - Theory Mathematical Physics 81T75, 81T13, 81T32, 46L87, 17B37 |
| url | https://arxiv.org/abs/2510.19112 |