报告人：Yongmin Cho 教授（韩国首尔国立大学）

题 目：Lectures on Theoretical Physics: Part One 理论物理学讲座：第一部分

时 间：2026年6月22-7月20日每周一、三、五

地 点：每周一1201、每周三1201、每周五1226

邀请人：刘玉孝、郭文帝

报告摘要：

The gauge theories play the fundamental role in theoretical physics. All four fundamental interactions in nature, gravitational, electromagnetic, weak, and strong interactions, are described by the gauge interaction. They are based on the gauge principle, which is essentially a part of the locality principle that tells that nature allows us the freedom to describe the physics locally in a different but consistent way. This is like different people at different places use different languages but they express the same feeling and same meaning in such a way that we can translate one language to another. This is the fundamental principle of equality and freedom, the principle of democracy of nature.

It took time for us to discover the gauge principle. In late nineteenth century people realized that the most effective and natural way to describe the electromagnetism is to use the Maxwell's potential, but it was known that different potentials could describe the same physical electromagnetic fields. In other words the physical fields could not fix the potential uniquely. This was the gauge degrees of freedom of the Maxwell's theory.

By early twentieth century it has become clear that this gauge freedom is a fundamental principle of theoretical physics, and the Yang-mills theory was constructed as a non-Abelian gauge theory. Moreover, even the Einstein's theory of gravitation was interpreted as a gauge theory of Lorentz group. Now, it is widely believed that all known fundamental interactions in nature are described by the gauge theory.

This is a lecture series on theoretical physics based on my personal preference. In the first part of this book we discuss the general aspects of gauge theories for later purpose. In Chapter I we review the basic features of the relativistic theory. In Chapter II we review the general aspects of Abelian gauge theory and gauge principle as a locality principle. In Chapter III we discuss the mass generation of Higgs mechanism without appealing to the spontaneous symmetry breaking. In Chapter IV we review the basic features of the non-Abelian gauge theories including the standard model which unifies the electromagnetic and weak interactions and the related theories. In Chapter V we review the Einstein's theory of gravitation, and derive the Einstein's general relativity as a gauge theory of Lorentz group. In Chapter VI we discuss the higher-dimensional unified theory of gauge theory with gravitation as the Einstein’s theory of gravitation of the (4+n)-dimensional unified space-time which admit the n-dimensional isometry. In Chapter VII we discuss the Abelian decomposition of the non-Abelian gauge theory which shows the skeleton structure of non-Abelian gauge theory. In Chapter VIII we discuss the vacuum structure of the non-Abelian gauge theory. Finally in Chapter IX we discuss the topological objects in non-Abelian gauge theories, in particular the two types of monopoles in the standard model.

规范理论在理论物理学中占据核心地位。自然界中存在的四种基本相互作用——引力、电磁、弱相互作用和强相互作用——均通过规范相互作用来描述。这些理论基于规范原理，该原理本质上是局域性原理的组成部分，其核心在于：自然界允许我们以不同但一致的方式对物理现象进行局部描述。这就好比不同地区的人使用不同的语言，却能表达相同的情感与意义，从而实现跨语言的精准传达。这正是平等与自由的根本原则，也是自然界的“民主性”原则。

我们花了相当长的时间才最终确立规范原理。19世纪末，人们认识到描述电磁学最有效且最自然的方法是使用麦克斯韦势；但当时已知不同的势函数均可描述相同的物理电磁场。换言之，物理场无法唯一确定某个特定的势函数——这正是麦克斯韦理论中的规范自由度。

到二十世纪初，人们已明确认识到这种规范自由性是理论物理学的基本原理之一，而杨-米尔斯理论正是作为非阿贝尔规范理论构建而成。此外，就连爱因斯坦的引力理论也被解释为洛伦兹群的规范理论。如今学界普遍认为，自然界中所有已知的基本相互作用均可通过规范理论来描述。

本系列讲座基于我个人的研究偏好，系统阐述理论物理学相关内容。本次讲座第一部分重点探讨规范理论的基本特征，为后续内容奠定基础：第一讲回顾相对论性理论的核心要素；第二讲解析阿贝尔规范理论的基本特性及其作为局域性原理的规范原理；第三讲探讨无需借助自发对称性破缺即可实现希格斯粒子质量生成机制；第四讲综述非阿贝尔规范理论的基础框架（包括统一电磁相互作用与弱相互作用的标准模型及相关理论）；第五讲回顾爱因斯坦引力理论，并推导出洛伦兹群规范理论下的广义相对论；第六讲研究高维统一规范理论——即以（4+n）维统一时空为背景、包含n维等距变换的爱因斯坦引力理论；第七讲剖析非阿贝尔规范理论的阿贝尔分解结构，揭示其核心骨架体系；第八讲探讨非阿贝尔规范理论中的真空结构；第九讲重点讨论非阿贝尔规范理论中的拓扑对象，特别是标准模型中的两种单极子类型。

报告人简介：

Yongmin Cho教授是第三世界科学院院士，韩国国家科学与工程院院士，亚太国际理论物理中心创始人，韩国首尔国立大学荣休教授。长期从事理论物理研究，在统一场论、高能物理、广义相对论和宇宙论领域均作出了突出的成就。欧洲核子中心（CERN）在发现“上帝粒子”--- Higgs粒子之后，建造了新的探测器--MoEDAL，寻找Yongmin Cho教授预言的新粒子--- Cho-Maison磁单极。