Ramond P. Group theory. A physicist's survey

Cambridge University Press, 2010. — 322 p.
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.PIERRE RAMOND is Distinguished Professor of Physics 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 supersymmetry, superstring theory and the theory of neutrino masses, and is a Member of the American Academy of Arts & Sciences.Preface: the pursuit of symmetries
Finite groups: an introduction
Finite groups: representations
Hilbert Spaces
SU(2)
SU(3)
Classification of compact simple Lie algebras
Lie algebras: representation theory
Finite groups: the road to simplicity
Beyond Lie algebras
The groups of the Standard Model
Exceptional structures
Appendices