标题： 李群及其在粒子物理中的应用：给物理专业本科生的教程 显示英文标题

标题： Lie Groups and their applications to Particle Physics: A Tutorial for Undergraduate Physics Majors

摘要： 对称性是当今粒子物理理论研究的核心。 我们的手稿是一篇教程，介绍理解物理对称性的基础数学知识。 我们从基本的群论和表示论开始。 然后介绍李群和李代数及其性质。 接下来详细讨论物理中的两个重要李群 特殊酉群和洛伦兹群，重点在于它们在粒子物理中的应用。 最后，我们介绍场论及其版本的 诺特定理。 我们认为，这里涵盖的材料将为本科生未来的数学物理学习做好准备。 显示英文摘要

摘要： Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory. We then introduce Lie Groups and Lie Algebra and their properties. We next discuss with detail two important Lie Groups in physics Special Unitary and Lorentz Group, with an emphasis on their applications to particle physics. Finally, we introduce field theory and its version of the Noether Theorem. We believe that the materials cover here will prepare undergraduates for future studies in mathematical physics.