One highly recommended book on group theory in the context of particle physics and quantum field theory (QFT) is "Lie Algebras in Particle Physics" by Howard Georgi. This book provides a comprehensive introduction to the mathematics of group theory and its applications to particle physics.
Here are some key features of the book:
Group Theory Basics: The book starts with an introduction to the basics of group theory, including symmetry operations, group representations, and Lie algebras. It explains the concepts in a clear and accessible manner, making it suitable for readers with different levels of mathematical background.
Particle Physics Applications: The book specifically focuses on the application of group theory to particle physics. It covers topics such as the SU(N) and SO(N) groups, their representations, and the connection between group theory and the fundamental forces of nature. It also explores the symmetry breaking mechanisms in particle physics.
Quantum Field Theory: The book goes beyond the scope of just group theory and delves into the application of group theory in quantum field theory. It discusses the gauge symmetries and their role in constructing the Standard Model of particle physics.
Problem Sets and Examples: Throughout the book, there are numerous problem sets and examples that help reinforce the concepts and develop a practical understanding of group theory in particle physics. These exercises are valuable for self-study and provide an opportunity for readers to apply the concepts to real-world scenarios.
"Lie Algebras in Particle Physics" is highly regarded in the physics community for its clarity, depth, and relevance to particle physics and QFT. It is suitable for graduate students and researchers in theoretical particle physics who want to develop a solid understanding of group theory and its applications in their field of study.