Symmetries, Lie algebras and representations : a graduate course for physicists
Jürgen Fuchs, Christoph Schweigert.
Cambridge : Cambridge University Press, 1997.
xxi, 438 págs. : ilustraciones ; 26 cm.
Serie: Cambridge monographs on mathematical physics
ISBN: 0521560012
Includes bibliographical references (p. 421-429) and index.
Reseña: MathSciNet, 99k:81078
Contenido
- 1. Symmetries and conservation laws
- 2. Basic examples
- 3. The Lie algebra $\germ{su}(3)$ 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.