规范场理论：各种数学方法
Gauge field theories: various mathematical approaches
摘要：
本文介绍了（经典）规范场理论，即常微分几何，非交换几何和传递李代数胚的相关现代数学公式。它们为杨-米尔斯-希格斯理论或引力理论提供了严格的描述框架，并且每一个都改进了规范场理论的范式。他们之间进行了简要的比较，主要是由于各种概念的连接。然而，它们揭示了一个令人信服的共同数学模式，本文就此得出结论。
英文摘要：
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
