Overview

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.

Full Product Details

Author:   Adam M. Bincer (Professor Emeritus, University of Wisconsin - Madison)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 19.20cm , Height: 1.70cm , Length: 24.70cm
Weight:   0.556kg
ISBN:  

9780199662920

ISBN 10:   0199662924
Pages:   216
Publication Date:   11 October 2012
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

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

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