Group Theory A Physicist's Survey

Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac–Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.

1. Preface: the pursuit of symmetries; 2. Finite groups: an introduction; 3. Finite groups: representations; 4. Hilbert Spaces; 5. SU(2); 6. SU(3); 7. Classification of compact simple Lie algebras; 8. Lie algebras: representation theory; 9. Finite groups: the road to simplicity; 10. Beyond Lie algebras; 11. The groups of the Standard Model; 12. Exceptional structures; Appendices; References; Bibliography; Index.

Designed for advanced undergraduate and graduate students, this book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. It gives a comprehensive overview of the main aspects of both finite and continuous group theory, highlighting applications to fundamental physics.

Pierre Ramond is a Distinguished Professor at the University of Florida and Director of the Institute for Fundamental Theory. He has held positions at FermiLab, Yale University and Caltech. He has made seminal contributions to Superstring Theory and the theory of neutrino masses, and is a member of the American Academy of Arts and Sciences.