Lie Groups and Lie Algebras - A Physicist's Perspective
By: Adam M. Bincer (author)Hardback
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This book is intended for graduate students in Physics. It starts with a discussion of angular momentum and rotations in terms of the orthogonal group in three dimensions and the unitary group in two dimensions and goes on to deal with these groups in any dimensions. All representations of su(2) are obtained and the Wigner-Eckart theorem is discussed. Casimir operators for the orthogonal and unitary groups are discussed. The exceptional group G2 is introduced as the group of automorphisms of octonions. The symmetric group is used to deal with representations of the unitary groups and the reduction of their Kronecker products. Following the presentation of Cartan's classification of semisimple algebras Dynkin diagrams are described. The book concludes with space-time groups - the Lorentz, Poincare and Liouville groups - and a derivation of the energy levels of the non-relativistic hydrogen atom in n space dimensions.
Adam Bincer is Professor Emeritus at University of Wisconsin - Madison.
1. Generalities ; 2. Lie Groups and Lie Algebras ; 3. Rotations: SO(3) an SU(2) ; 4. Representations of SU(2) ; 5. The so(n) Algebra and Clifford Numbers ; 6. Reality Properties of Spinors ; 7. Clebsch-Gordan Series for Spinors ; 8. The Center and Outer Automorphisms of Spin(n) ; 9. Composition Algebras ; 10. The Exceptional Group G2 ; 11. Casimir Operators for Orthogonal Groups ; 12. Classical Groups ; 13. Unitary Groups ; 14. The Symmetric Group Sr and Young Tableaux ; 15. Reduction of SU(n) Tensors ; 16. Cartan Basis, Simple Roots and Fundamental Weights ; 17. Cartan Classification of Semisimple Algebras ; 18. Dynkin Diagrams ; 19. The Lorentz Group ; 20. The Poincare and Liouville Groups ; 21. The Coulomb Problem in n Space Dimensions
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- ID: 9780199662920
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