Group Theory and Physics
by: S. Sternberg
Product Details
* ISBN: 0521248701
ISBN-13: 9780521248709
* Format: Hardcover, 443pp
* Publisher: Cambridge University Press
Table of Contents Preface 1 Basic definitions and examples 1 1.1 Groups: definition and examples 1 1.2 Homomorphisms: the relation between SL(2,C) and the Lorentz group 6 1.3 The action of a group on a set 12 1.4 Conjugation and conjugacy classes 14 1.5 Applications to crystallography 16 1.6 The topology of SU(2) and SO(3) 21 1.7 Morphisms 24 1.8 The classification of the finite subgroups of SO(3) 27 1.9 The classification of the finite subgroups of O(3) 33 1.10 The icosahedral group and the fullerenes 43 2 Representation theory of finite groups 48 2.1 Definitions, examples, irreducibility 48 2.2 Complete reducibility 52 2.3 Schur's lemma 55 2.4 Characters and their orthogonality relations 58 2.5 Action on function spaces 60 2.6 The regular representation 64 2.7 Character tables 69 2.8 The representations of the symmetric group 76 3 Molecular vibrations and homogeneous vector bundles 94 3.1 Small oscillations and group theory 94 3.2 Molecular displacements and vector bundles 97 3.3 Induced representations 104 3.4 Principal bundles 112 3.5 Tensor products 115 3.6 Representative operators and quantum mechanical selection rules 116 3.7 The semiclassical theory of radiation 129 3.8 Semidirect products and their representations 135 3.9 Wigner's classification of the irreducible representation of the Poincare group 143 3.10 Parity 150 3.11 The Mackey theorems on induced representations, with applications to the symmetric group 161 3.12 Exchange forces and induced representations 168 4 Compact groups and Lie groups 172 4.1 Haar measure 173 4.2 The Peter-Weyl theorem 177 4.3 The irreducible representations of SU(2) 181 4.4 The irreducible representations of SO(3) and spherical harmonics 185 4.5 The hydrogen atom 190 4.6 The periodic table 198 4.7 The shell model of the nucleus 208 4.8 The Clebsch-Gordan coefficients and isospin 213 4.9 Relativistic wave equations 225 4.10 Lie algebras 234 4.11 Representations of su(2) 238 5 The irreducible representations of SU(n) 246 5.1 The representation of Gl(V) on the r-fold tensor product 246 5.2 Gl(V) spans Hom[subscript Sr] (T[subscript r]V, T[subscript r]V) 248 5.3 Decomposition of T[subscript r]V into irreducibles 250 5.4 Computational rules 252 5.5 Description of tensors belonging to W[lambda] 254 5.6 Representations of Gl(V) and Sl(V) on U[lambda] 258 5.7 Weight vectors 263 5.8 Determination of the irreducible finite-dimensional representations of Sl(d,C) 266 5.9 Strangeness 275 5.10 The eight-fold way 284 5.11 Quarks 288 5.12 Color and beyond 297 5.13 Where do we stand? 300 Appendix A: The Bravais lattices and the arithmetical crystal classes 309 Appendix B: Tensor product 320 Appendix C: Integral geometry and the representations of the symmetric group 327 Appendix D: Wigner's theorem on quantum mechanical symmetries 354 Appendix E: Compact groups, Haar measure, and the Peter-Weyl theorem 359 Appendix F: A history of 19th century spectroscopy 382 Appendix G: Characters and fixed point formulas for Lie groups 407 Further reading 424 Index 428
http://ifile.it/7atdf4/sternberg_s_-_group_theory_and_physics_cup_1994.pdf
