We describe gauge symmetry at the elementary level aiming at undergraduate and first-year graduate theoretical physics students. The formal definition of gauge invariance as a local symmetry of the action is given and further elaborated and interpreted in detail in two physical models, namely, a mechanical system and the prototypical gauge field theory of electrodynamics. The first model, consisting of two interacting particles with gauge symmetry, sets the background and paves the way for the canonical analysis of the electromagnetic field as a constrained system. The Dirac–Bergmann algorithm and the necessity of Dirac brackets for the canonical quantization of constrained systems are discussed within the two models context. The whole analysis is written in a didactical way trying to guide and motivate undergraduate students along an introduction to gauge symmetry. After going through this present brief introduction, the reader should be well prepared to boldly continue their journey through more advanced standard textbooks on the subject.

我们针对本科生和一年级研究生理论物理学生描述了基本水平的规范对称性。规范不变性的正式定义为作用的局部对称性，并在机械系统和电动力学的原型规范场理论这两个物理模型中进一步详细阐述和解释。第一个模型由两个具有规范对称性的相互作用粒子组成，为作为约束系统的电磁场的规范分析奠定了背景并铺平了道路。狄拉克-伯格曼算法和狄拉克括号对约束系统的规范量化的必要性在两个模型上下文中进行了讨论。整个分析以教学的方式编写，试图通过介绍规范对称性来指导和激励本科生。在阅读完本简要介绍之后，读者应该做好充分准备，大胆地继续阅读有关该主题的更高级的标准教科书。