Group theory and its application to physical problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Dover Publications, Inc.
1989
|
| Edition: | unabridged, corrected republication of the second (corrected) printing (1964) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 509 Seiten Illustrationen |
| ISBN: | 0486661814 9780486661810 |
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MARC
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| 100 | 1 | |a Hamermesh, Morton |d 1915-2003 |e Verfasser |0 (DE-588)1078419302 |4 aut | |
| 245 | 1 | 0 | |a Group theory and its application to physical problems |c by Morton Hamermesh |
| 250 | |a unabridged, corrected republication of the second (corrected) printing (1964) | ||
| 264 | 1 | |a New York |b Dover Publications, Inc. |c 1989 | |
| 264 | 4 | |c © 1962 | |
| 300 | |a xv, 509 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Groepentheorie |2 gtt | |
| 650 | 7 | |a Groupes, Théorie des |2 ram | |
| 650 | 7 | |a Mathematische fysica |2 gtt | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Group theory | |
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Record in the Search Index
| _version_ | 1817983092397178880 |
|---|---|
| adam_text |
CONTENTS
Introduction
.
Chapter
1. Elements
of Gboup Theoey
. 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
Є»
. 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-Ю
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 spaces; scalar product; unitary matrices; Hermitian
matrices
. 88
3-Ю
Operators: adjoint, self-adjoint, unitary
. 91
vii
Il CONTENTS
3-11
Unitary representations
. 92
3-12
Hubert 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
6.
Miscellaneous Operations with Grotjp
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
S„.
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 Gboups
. 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 Spheeical 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
CONTENTS
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
Chapteb
10.
Linear Groups in ^-Dimensional Space.
Irreducible
Tensões
. 377
10-1
Tensors with respect to GL(n)
. 377
10-2
The construction of irreducible tensors with respect to GL(ri)
. 378
10-3
The dimensionality of the irreducible representations of GL(n)
. 384
10-4
Irreducible representations of subgroups of GL(n): SL(n),
V(n),SU(n)
. 388
10-5
The orthogonal group in
η
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 0+(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
S U(n)
. 413
11-2
Angular momentum analysis. Decomposition of representations
of 8U(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 ¿'-coupling
. 430
11-6
Nuclear structure.
Isotopie
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 ¿-coupling shell model. Seniority in ¿"-coupling
. . · 448
Chapteb
12.
Ray Representations. Little Gboups
. 458
12-1
Projective
representations of finite groups
. 458
12-2
Examples of protective representations of finite groups
. . . 463
12-3
Ray representations of Lie groups
. 469
CONTENTS Xl
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
Bibliography and Notes
. 499
Index
. 505 |
| any_adam_object | 1 |
| author | Hamermesh, Morton 1915-2003 |
| author_GND | (DE-588)1078419302 |
| author_facet | Hamermesh, Morton 1915-2003 |
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| ctrlnum | (OCoLC)20218471 (DE-599)BVBBV004288966 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | unabridged, corrected republication of the second (corrected) printing (1964) |
| format | Book |
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| id | DE-604.BV004288966 |
| illustrated | Illustrated |
| indexdate | 2024-12-09T17:03:02Z |
| institution | BVB |
| isbn | 0486661814 9780486661810 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002667791 |
| oclc_num | 20218471 |
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| owner | DE-384 DE-739 DE-355 DE-BY-UBR DE-20 |
| owner_facet | DE-384 DE-739 DE-355 DE-BY-UBR DE-20 |
| physical | xv, 509 Seiten Illustrationen |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Dover Publications, Inc. |
| record_format | marc |
| spelling | Hamermesh, Morton 1915-2003 Verfasser (DE-588)1078419302 aut Group theory and its application to physical problems by Morton Hamermesh unabridged, corrected republication of the second (corrected) printing (1964) New York Dover Publications, Inc. 1989 © 1962 xv, 509 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Groepentheorie gtt Groupes, Théorie des ram Mathematische fysica gtt Physique mathématique ram Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Physik (DE-588)4045956-1 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002667791&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 1915-2003 Group theory and its application to physical problems Groepentheorie gtt Groupes, Théorie des ram Mathematische fysica gtt Physique mathématique ram Group theory 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 | Groepentheorie gtt Groupes, Théorie des ram Mathematische fysica gtt Physique mathématique ram Group theory Gruppentheorie (DE-588)4072157-7 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Groepentheorie Groupes, Théorie des Mathematische fysica Physique mathématique Group theory Gruppentheorie Physik |
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