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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 |
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Add Group Theory and Physics, This book is an introduction to group theory and its application to physics. The author considers the physical applications and develops mathematical theory in a presentation that is unusually cohesive and well-motivated. The book discusses many modern to, Group Theory and Physics to the inventory that you are selling on WonderClubX
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Add Group Theory and Physics, This book is an introduction to group theory and its application to physics. The author considers the physical applications and develops mathematical theory in a presentation that is unusually cohesive and well-motivated. The book discusses many modern to, Group Theory and Physics to your collection on WonderClub |