Lie Groups and Lie Algebras - A Physicist's Perspective [Hardcover]

This book is intended for graduate students in Physics, especially Elementary Particle Physics. It gives an introduction to group theory for physicists with a focus on Lie groups and Lie algebras.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.1. Generalities2. Lie Groups and Lie Algebras3. Rotations: SO(3) an SU(2)4. Representations of SU(2)5. The so(n) Algebra and Clifford Numbers6. Reality Properties of Spinors7. Clebsch-Gordan Series for Spinors8. The Center and Outer Automorphisms of Spin(n)9. Composition Algebras10. The Exceptional Group G211. Casimir Operators for Orthogonal Groups12. Classical Groups13. Unitary Groups14. The Symmetric Group Sr and Young Tableaux15. Reduction of SU(n) Tensors16. Cartan Basis, Simple Roots and Fundamental Weights17. Cartan Classification of Semisimple Algebras18. Dynkin Diagrams19. The Lorentz Group20. The Poincare and Liouville Groups21. The Coulomb Problem in n Space DimensionsAdam Bincer is Professor Emeritus at University of Wisconsin - Madison.It gives an introduction to group theory for physicists with a focus on Lie groups and Lie algebras.