Lie Groups and Lie Algebras - A Physicist's Perspective A Physicist's Perspective

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 - 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

Adam Bincer is Professor Emeritus at University of Wisconsin - Madison.