Title: Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview Show Chinese title

Title: 非对易规范理论：杨-米尔斯扩展及其他——综述

Abstract: 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 $\mathbb{R}^3_\lambda$, 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 $\kappa$-Minkowski. Show Chinese abstract

Abstract: 几种代表性规范理论在各种量子时空上的状态，主要集中在Yang-Mills类型扩展以及一些矩阵模型公式上进行了概述。 共同的构建模块是基于导数的微分微积分，可能是扭曲的和非交换的Koszul连接的类似物。 与量子时空相关的乘积是从群代数的调和分析与Weyl量子化的结合中得到的。 概述了在两种不同公式下Moyal空间上规范理论固有的剩余问题。 在$\mathbb{R}^3_\lambda$上提出了一族规范不变的矩阵模型，这是$\mathbb{R}^3$的一个变形，其中包括一个可解模型。 通过它们的$*$-代数对11个新的量子闵可夫斯基时空进行了表征。 在一个最近研究的这些时空之一上构造了一个Yang-Mills类型的规范理论，并与其在流行的$\kappa$-闵可夫斯基上构建的对应理论进行了比较。