Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists (Cambridge Monographs on Mathematical Physics)
Cambridge University Press, 6/13/2014
EAN 9780521541190, ISBN10: 0521541190
Paperback, 100 pages, 24.6 x 18.9 x 2.7 cm
Language: English
Originally published in English
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.
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.