Symmetries, Lie Algebras and Representations
Symmetries, Lie Algebras and Representations
Christoph Schweigert, Institut des Hautes Études Scientifiques, France
This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers.
- Many exercises and tips
- Clear pedagogical style with many exercises and extensive references
- Fuchs is an experienced author with a very successful book in this area already published
- 'Extras' available from the author's web site
Reviews & endorsements
'One finds a striking wealth of material in this book … The reviewer wholeheartedly recommends this text to graduate students as well as to researchers in theoretical physics and related areas.' Acta. Sci. Math
'The presentation of material is next to perfect, … this book may be considered as an excellent textbook … I agree with the authors that 'many readers will even use it as a reference tool for their whole professional life'.' Vladimir D. Ivashchuk, General Relativity and Gravitation
Product details
No date availablePaperback
9780521541190
464 pages
246 × 189 × 26 mm
0.816kg
36 b/w illus. 18 tables 188 exercises
Table of Contents
- Preface
- 1. Symmetries and conservation laws
- 2. Basic examples
- 3. The Lie algebra su(3) and hadron symmetries
- 4. Formalization: algebras and Lie algebras
- 5. Representations
- 6. The Cartan-Weyl basis
- 7. Simple and affine Lie algebras
- 8. Real Lie algebras and real forms
- 9. Lie groups
- 10. Symmetries of the root system. The Weyl group
- 11. Automorphisms of Lie algebras
- 12. Loop algebras and central extensions
- 13. Highest weight representations
- 14. Verma modules, Casimirs, and the character formula
- 15. Tensor products of representations
- 16. Clebsch-Gordan coefficients and tensor operators
- 17. Invariant tensors
- 18. Subalgebras and branching rules
- 19. Young tableaux and the symmetric group
- 20. Spinors, Clifford algebras, and supersymmetry
- 21. Representations on function spaces
- 22. Hopf algebras and representation rings
- Epilogue
- References
- Index.
