LOMONT - APPLICATIONS of FINITE GROUPS

08-02-2014, 6:52
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Stan: Używany
Okładka: twarda
Język: angielski

"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