Group Theory
A Physicist's Survey

For advanced undergraduates and graduates, introducing physicists to the mathematical aspects of group theory, and mathematicians to its physics applications.

Pierre Ramond (Author)

9780521896030, Cambridge University Press

Hardback, published 13 May 2010

322 pages, 65 b/w illus.
25.5 x 17.8 x 1.9 cm, 0.78 kg

"The books construction is straightforward... Group Theory: A Physicist's Survey successfully introduces physics model builder to the most likely toold os choice for future constructions."
Robert Gilmore, Physics Today

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.

Subject Areas: Maths for engineers [TBJ], Mathematical physics [PHU], Algebra [PBF]