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

TL;DR

This tutorial introduces undergraduate physics students to the mathematical foundations of symmetry in particle physics, focusing on Lie groups, Lie algebras, and their applications, including the Lorentz and Special Unitary groups, culminating in field theory and Noether's theorem.

Contribution

It provides a comprehensive, accessible introduction to Lie groups and their role in particle physics tailored for undergraduate students, bridging foundational mathematics and physical applications.

Findings

Detailed explanation of Lie groups and Lie algebras

Application of Lie groups to Lorentz and Special Unitary groups

Introduction to Noether's theorem in field theory

Abstract

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.