|
|
"APPLICATIONS of FINITE GROUPS", J.S.LOMONT; ACADEMIC PRESS, NOWY JORK, LONDYN; stan : plus db : pieczątki ; przesyłka polecona : 8,00 zł.
CONTENTS :
Preface V
List of Symbols xi
I. MATRICES 1
II. GROUPS 17
1. Abstract Properties 17
2. Applications 36
A. Thermodynamics 36
B. The Dirac Eąuation 40
C. Fermion Annihilation and Creation Operators 42
III. REPRESENTATIONS 46
1. Matrix Groups 46
2. The Key Theorem of Representation Theory 52
3. Character Tables 56
4. Computation of Character Tables 61
5. Properties of Character Tables 64
6. Faithful Representations 68
7. Kronecker Products 69
8. Simply Reducible Groups 70
9. Reduction by Idempotents 71
10. Groups of Mathernatical Physics 78
A. Cyclic Groups 78
B. Dihedral Groups 78
C. Tetrahedral Group 81
D. Octahedral Group 81
E. Icosahedral Group 82
11. Tensors and Invariants 82
12. Representations Generated by Functions 84
13. Subduced Representations 89
IV. APPLICATIONS 92
1. Fermion Annihilation and Creation Operators 92
2. Molecular Vibrations (Classical) 96
3. Symmetric Waveguide Junctions 126
4. Crystallographic Point Groups 132
5. Proportionality Tensors in Crystals 146
6. The Three-Dimensional Rotation Group 149
7. Double Point Groups 161
8. Nonrelativistic Wave Equations 167
9. Stationary Perturbation Theory 177
10. Lattice Harmonics 188
11. Molecular Orbitals 190
12. Crystallographic Lattices 198
13. Crystallographic Space Groups 202
14. Wave Functions in Crystals 206
V. SUBGROUPS AND REPRESENTATIONS 219
1. Subduced Representations 219
2. Induced Representations 223
3. Induced and Subduced Representations 226
4. Projective Representations 227
5. Little Groups 230
VI. SPACE GROUP REPRESENTATIONS AND ENERGY BANDS 236
1. Representation Theory 236
2. Example—Two-Dimensional Sąuare Lattice 238
3. Reality of Representations 246
4. Analysis 252
5. Compatibility 254
6. Physics 256
VII. SYMMETRIC GROUPS 258
1. Abstract Properties of S(n) 259
2. Representations of S(n) 261
3. Miscellany and the Fuli Linear Groups 266
4. Construction of Irreducible Representations of the Symmetric Groups 271
VIII. APPLICATIONS 274
1. Permutation Degeneracy and the Pauli Exclusion Principle 274
2. Atomie Structure 276
A. The Central Field Approximation 277
B. LS Coupling 279
3. Multiplet Splittmg in Crystalline Electric Fields 284
4. Molecular Structure 285
5. Nuclear Structure 291
A. Spatial Coordinate Approximation 292
B. Spin Approximation 294
6. Selection Rules 295
References 299
Appendix I: Proof of the Key Theorem of Representation Theory 308
Appendix II: Irreducible Representations of D3, D4, D6, T, O, and S 312
Appendix III: The Lorentz Groups 315
Subject Index 341 |
|
|
