Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview

Fuente: arXiv
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Main Author: Wallet, Jean-Christophe
Format: Preprint
Published: 2025
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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