Group Theory in Physics: An Introduction with Mathematica

TL;DR

This paper introduces a comprehensive Mathematica-based educational resource for understanding Group Theory in physics, including examples on various groups and applications like angular momentum and spacetime transformations.

Contribution

It provides a unified, beginner-friendly collection of Mathematica notebooks demonstrating core Group Theory concepts and their applications in physics education.

Findings

Includes example notebooks for finite, compact, and non-compact groups.

Demonstrates applications in angular momentum addition and qubit modeling.

Facilitates learning through adaptable, well-structured educational materials.

Abstract

Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various packages and built-in tools for Group Theory. However, these resources are often too scattered for effective educational use. This work aims to provide a comprehensive source to help beginning students grasp Group Theory concepts and their applications from a physicist's perspective, while also building familiarity with symbolic language. We present several example notebooks that succinctly cover well-known theories and demonstrate specific concepts, which can be easily adapted for educational purposes. We provide basic examples on finite, compact and non-compact groups, and motivate the use of these concepts in solving physics problems such as addition of angular momenta, modelling a system of qubits and the description of spacetime transformations.