Group theory and its application to physical problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1964
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| Ausgabe: | 2. print. |
| Schriftenreihe: | Addison-Wesley series in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 509 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Group theory and its application to physical problems |c by Morton Hamermesh |
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| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1964 | |
| 300 | |a XV, 509 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804140057514213376 |
|---|---|
| adam_text | CONTENTS
Introduction xiii
Chapter 1. Elements of Group Theory 1
1-1 Correspondences and transformations 1
1-2 Groups. Definitions and examples 6
1-3 Subgroups. Cayley s theorem 15
1-4 Cosets. Lagrange s theorem 20
1-5 Conjugate classes 23
1-6 Invariant subgroups. Factor groups. Homomorphism ... 28
1-7 Direct products 30
Chapter 2. Symmetry Groups 32
2-1 Symmetry elements. Pole figures 32
2-2 Equivalent axes and planes. Two-sided axes 38
2-3 Groups whose elements are pure rotations: uniaxial groups,
dihedral groups 41
2-4 The law of rational indices 45
2-5 Groups whose elements are pure rotations. Regular polyhedra . 48
2-6 Symmetry groups containing rotation reflections. Adjunction
of reflections to C 52
2-7 Adjunction of reflections to the groups Dn 55
2-8 The complete symmetry groups of the regular polyhedra . . 58
2-9 Summary of point groups. Other systems of notation ... 60
2-10 Magnetic symmetry groups (color groups) 63
Chapter 3. Group Representations 68
3-1 Linear vector spaces 68
3-2 Linear dependence; dimensionality 70
3-3 Basis vectors (coordinate axes); coordinates 71
3-4 Mappings; linear operators; matrix representations; equivalence 74
3-5 Group representations 77
3-6 Equivalent representations; characters 79
3-7 Construction of representations. Addition of representations . 80
3-8 Invariance of functions and operators. Classification of
eigenfunctions 86
3-9 Unitary spaees; scalar product; unitary matrices; Hermitian
matrices 88
3-10 Operators: adjoint, self-adjoint, unitary 91
vii
Viii CONTENTS
3-11 Unitary representations 92
3-12 Hilbert space 93
3-13 Analysis of representations; reducibility; irreducible
representations 94
3-14 Schur s lemmas 98
3-15 The orthogonality relations 101
3-16 Criteria for irreducibility. Analysis of representations . . . 104
3-17 The general theorems. Group algebra 106
3-18 Expansion of functions in basis functions of irreducible
representations Ill
3-19 Representations of direct products 114
Chapter 4. Irreducible Representations of the Point
Symmetry Groups 115
4-1 Abelian groups 115
4-2 Nonabelian groups 119
4-3 Character tables for the crystal point groups 125
Chapter 5. Miscellaneous Operations with Group
Representations 128
5-1 Product representations (Kronecker products) 128
5-2 Symmetrized and antisymmetrized products . . . . . . 132
5-3 The adjoint representation. The complex conjugate
representation 135
5-4 Conditions for existence of invariants 136
5-5 Real representations 138
5-6 The reduction of Kronecker products. The Clebsch-Gordan
series 147
5-7 Clebsch-Gordan coefficients 148
5-8 Simply reducible groups •. 151
5-9 Three-j symbols 156
Chapter 6. Physical Applications 161
6-1 Classification of spectral terms 161
6-2 Perturbation theory 162
6-3 Selection rules 166
6-4 Coupled systems 178
Chapter 7. The Symmetric Group 182
7-1 The deduction of the characters of a group from those
of a subgroup 182
CONTENTS ix
7-2 Frobenius formula for the characters of the symmetric group . 189
7-3 Graphical methods. Lattice permutations. Young patterns.
Young tableaux 198
7-4 Graphical method for determining characters 201
7-5 Recursion formulas for characters. Branching laws .... 208
7-6 Calculation of characters by means of the Frobenius formula . 212
7-7 The matrices of the irreducible representations of Sn-
Yamanouchi symbols 214
7-8 Hund s method 231
7-9 Group algebra 239
7-10 Young operators 243
7-11 The construction of product wave functions of a given symmetry.
Fock s cyclic symmetry conditions 246
7-12 Outer products of representations of the symmetric group . . 249
7-13. Inner products. Clebsch-Gordan series for the symmetric group 254
7-14 Clebsch-Gordan (CG) coefficients for the symmetric group.
Symmetry properties. Recursion formulas 260
Chapter 8. Continuous Geoups 279
8-1 Summary of results for finite groups 279
8-2 Infinite discrete groups 281
8-3 Continuous groups. Lie groups 283
8-4 Examples of Lie groups 287
8-5 Isomorphism. Subgroups. Mixed continuous groups . . . 291
8-6 One-parameter groups. Infinitesimal transformations . . . 293
8-7 Structure constants 299
8-8 Lie algebras 301
8-9 Structure of Lie algebras 304
8-10 Structure of compact semisimple Lie groups and their algebras . 309
8-11 Linear representations of Lie groups 311
8-12 Invariant integration 313
8-13 Irreducible representations of Lie groups and Lie algebras.
The Casimir operator 317
8-14 Multiple-valued representations. Universal covering group . . 319
Chapter 9. Axial and Spherical Symmetry 322
9-1 The rotation group in two dimensions 322
9-2 The rotation group in three dimensions 325
9-3 Continuous single-valued representations of the three-
dimensional rotation group 333
9-4 Splitting of atomic levels in crystalline fields (single-valued
representations) 337
9-5 Construction of crystal eigenfunctions 342
X CONTEXTS
9-6 Two-valued representations of the rotation group. The unitary
unimodular group in two dimensions 348
9-7 Splitting of atomic levels in crystalline fields. Double-valued
representations of the crystal point groups 357
9-8 Coupled systems. Addition of angular momenta. Clebsch-
Gordan coefficients 367
Chapter 10. Linear Groups ix w-Dimensional Space.
Irreducible Tensors 377
10-1 Tensors with respect to GL(n) 377
10-2 The construction of irreducible tensors with respect to GL(n) . 378
10-3 The dimensionality of the irreducible representations of GL(n) . 384
10-4 Irreducible representations of subgroups of GL{n): SL(n),
U(n), SU(n) 388
10-5 The orthogonal group in n dimensions. Contraction. Traceless
tensors 391
10-6 The irreducible representations of O(n) 394
10-7 Decomposition of irreducible representations of U(n) with
respect to O+(n) 399
10-8 The symplectic group Sp(n). Contraction. Traceless Tensors . 403
10-9 The irreducible representations of Sp{n). Decomposition of
irreducible representations of U(n) with respect to its
symplectic subgroup 408
Chapter 11. Applications to Atomic and Nuclear Problems . . 413
11—1 The classification of states of systems of identical particles
according to SU{7i) 413
11-2 Angular momentum analysis. Decomposition of representations
of S U{n) into representations of O+(3) 414
11-3 The Pauli principle. Atomic spectra in Russell-Saunders
coupling 417
11-4 Seniority in atomic spectra 423
11-5 Atomic spectra in jj-coupling 430
11-6 Nuclear structure. Isotopic spin 433
11-7 Nuclear spectra in L-S coupling. Supermultiplets .... 435
11-8 The L-S coupling shell model. Seniority 443
11-9 The jj-coupling shell model. Seniority in jj-coupling . . . 448
Chapter 12. Ray Representations. Little Groups 458
12-1 Protective representations of finite groups 458
12-2 Examples of protective representations of finite groups . . . 463
12-3 Ray representations of Lie groups 469
CONTENTS xi
12-4 Ray representations of the pseudo-orthogonal groups .... 478
12—5 Ray representations of the Galilean group 484
12-6 Irreducible representations of translation groups 486
12-7 Little groups 489
blbliogkaphy and notes 499
Index 505
|
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| discipline | Mathematik |
| edition | 2. print. |
| format | Book |
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| physical | XV, 509 S. graph. Darst. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Addison-Wesley |
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| series2 | Addison-Wesley series in physics |
| spelling | Hamermesh, Morton Verfasser aut Group theory and its application to physical problems by Morton Hamermesh 2. print. Reading, Mass. [u.a.] Addison-Wesley 1964 XV, 509 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in physics Physik (DE-588)4045956-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Physik (DE-588)4045956-1 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018054800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hamermesh, Morton Group theory and its application to physical problems Physik (DE-588)4045956-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4045956-1 (DE-588)4072157-7 |
| title | Group theory and its application to physical problems |
| title_auth | Group theory and its application to physical problems |
| title_exact_search | Group theory and its application to physical problems |
| title_full | Group theory and its application to physical problems by Morton Hamermesh |
| title_fullStr | Group theory and its application to physical problems by Morton Hamermesh |
| title_full_unstemmed | Group theory and its application to physical problems by Morton Hamermesh |
| title_short | Group theory and its application to physical problems |
| title_sort | group theory and its application to physical problems |
| topic | Physik (DE-588)4045956-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Physik Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018054800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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