论文标题
谎言组及其对粒子物理的应用：本科生专业的教程
Lie Groups and their applications to Particle Physics: A Tutorial for Undergraduate Physics Majors
论文作者
论文摘要
对称是粒子物理学当今理论研究的核心。我们的手稿是一个介绍基础数学的教程，用于理解物理对称性。我们从基本的群体理论和表示理论开始。然后，我们介绍谎言组并说谎代数及其特性。接下来，我们详细讨论物理特殊统一和洛伦兹组的两个重要谎言组，重点是它们在粒子物理学上的应用。最后，我们介绍了现场理论及其版本的Noether定理。我们认为，这里的材料覆盖将为将来的数学物理学研究做准备。
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.
