Non-Abelian optics has emerged as a promising research field with the potential to revolutionize our understanding of light–matter interactions and enable new applications in areas including topological photonic devices, quantum computing, optical sensing, and communications. This review provides an overall framework for the rapidly developing field of non-Abelian properties in optics, including the basic concepts of non-Abelian optics, the physical mechanism of non-Abelian statistics, the non-Abelian gauge field in optics, non-Abelian braiding in optics as a special phenomenon of the non-Abelian gauge field, and current challenges and opportunities. This review is intended to provide a new perspective on non-Abelian optics, summarize the current status and advanced progress in non-Abelian gauge fields and braiding in optics, and stimulate dialog about future perspectives.

中文翻译：

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光学中的非阿贝尔规范场

非阿贝尔光学已成为一个有前途的研究领域，有可能彻底改变我们对光与物质相互作用的理解，并在拓扑光子器件、量子计算、光学传感和通信等领域实现新的应用。该综述为快速发展的光学非阿贝尔性质领域提供了总体框架，包括非阿贝尔光学的基本概念、非阿贝尔统计的物理机制、光学中的非阿贝尔规范场、非阿贝尔光学光学中的编织作为非阿贝尔规范场的一种特殊现象，以及当前的挑战和机遇。本文旨在为非阿贝尔光学提供新的视角，总结非阿贝尔规范场和光学编织的现状和进展，并激发关于未来观点的对话。