Group theory and its application to physical problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1964
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| Edition: | 2. print. |
| Series: | Addison-Wesley series in physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 509 S. |
| ISBN: | 0201027801 |
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MARC
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| 245 | 1 | 0 | |a Group theory and its application to physical problems |c by Morton Hamermesh |
| 250 | |a 2. print. | ||
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| 300 | |a XV, 509 S. | ||
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Record in the Search Index
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|---|---|
| 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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| bvnumber | BV005685189 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)257422617 (DE-599)BVBBV005685189 |
| discipline | Mathematik |
| edition | 2. print. |
| format | Book |
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| id | DE-604.BV005685189 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:07Z |
| institution | BVB |
| isbn | 0201027801 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003551107 |
| oclc_num | 257422617 |
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| owner_facet | DE-703 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-384 |
| physical | XV, 509 S. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Addison-Wesley |
| record_format | marc |
| 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. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in physics Physik - Gruppentheorie Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Physik (DE-588)4045956-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003551107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hamermesh, Morton Group theory and its application to physical problems Physik - Gruppentheorie Gruppentheorie (DE-588)4072157-7 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4045956-1 |
| 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 - Gruppentheorie Gruppentheorie (DE-588)4072157-7 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Physik - Gruppentheorie Gruppentheorie Physik |
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