纤维丛、规范场和杨-米尔斯方程之间的类比--学科融合研究的一条途径  

The analogy between fiber bundle,gauge field and Yang-Mills equation-A way of disciplinary integration research

作　　者：赵松年[1] 路博 陈肯 黄旭 ZHAO Song-nian;LU Bo;CHEN Ken;HUANG Xu(Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,China;College of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]中国科学院大气物理研究所,北京100029 [2]北京邮电大学理学院,北京100876

出　　处：《大学物理》2022年第6期16-25,共10页College Physics

基　　金：国家自然科学基金(62071488)资助。

摘　　要：现在,规范场是物理学中重要的研究领域,而纤维丛则是数学中的热门课题.从本质上讲,就是杨-米尔斯方程将规范场与纤维丛二者联系起来,成为它们的理论的发端.本文着重从物理概念出发,分别论述规范场在物理学中、纤维丛在微分几何中相关概念的形成、发展,以及其与杨-米尔斯方程之间的关系,以使更多的相关专业读者能在这一重要的领域中产生探索和创新的热情,进行深入的研究,促进它在物理、数学和相互交叉课题中取得进展.特别是通过矢量势的旋度运算给出杨-米尔斯方程的一种新的数学表达形式,阐明了它的空间属性,由此能更好地将这三者联系起来,可以加深对纤维丛的联络在更深层次的了解,由于此类问题是一个新的研究方向,值得有志者去深入探索.The gauge field is an important research field in physics,and the fiber bundle is a hot topic in mathematics.Essentially,it is the Yang-Mills equation that connects the gauge field and the fiber bundle and becomes their theoretical basis.This paper focuses on the physical concept and discusses the gauge field in physics and the fiber bundle in differential geometry.The formation and development of related concepts,and the relationship with the Yang-Mills equation,so that more readers can inspire the enthusiasm of exploration and innovation in this important field,conduct in-depth research,and promote its use in physics and mathematics.Making progress in intersecting topics,especially by linking the three through the curl calculation of the vector potential,can deepen a deeper understanding of the connection of fiber bundles,because this type of problem is a new research direction.Among them,there are still many questions,which are worthy of in-depth exploration by those with lofty ideals.

关 键 词：纤维丛 规范场 联络 转动群 对称性 不变性 

分 类 号：O4-1[理学—物理]