Problems & solutions in group theory for physicists:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2007
|
| Ausgabe: | Reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 464 S. |
| ISBN: | 981238832X 9812388338 9789812388339 |
Internformat
MARC
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| 245 | 1 | 0 | |a Problems & solutions in group theory for physicists |c Zhong-Qi Ma ; Xiao-Yan Gu |
| 250 | |a Reprint. | ||
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2007 | |
| 300 | |a X, 464 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
v
1. REVIEW
ON LINEAR ALGEBRAS
1
1.1
Eigenvalues and Eigenvectors of a Matrix
.......... 1
1.2
Some Special Matrices
..................... 4
1.3
Similarity Transformation
................... 7
2.
GROUP AND ITS SUBSETS
27
2.1
Definition of a Group
...................... 27
2.2
Subsets in a Group
....................... 29
2.3
Homomorphism of Groups
................... 33
3.
THEORY OF REPRESENTATIONS
43
3.1
Transformation Operators for a Scalar Function
....... 43
3.2
Inequivalent and Irreducible Representations
........ 47
3.3
Subduced and Induced Representations
........... 65
3.4
The Clebsch-Gordan Coefficients
............... 79
4.
THREE-DIMENSIONAL ROTATION GROUP
115
4.1
SO(3) Group and Its Covering Group SU(2)
......... 115
4.2
Inequivalent and Irreducible Representations
........ 123
4.3
Lie Groups and Lie Theorems
................. 140
4.4
Irreducible Tensor Operators
................. 146
4.5
Unitary Representations with Infinite Dimensions
...... 166
5.
SYMMETRY OF CRYSTALS
173
5.1
Symmetric Operations and Space Groups
.......... 173
χ
Problems
and Solutions in Group Theory
5.2
Symmetric Elements
...................... 177
5.3
International Notations for Space Groups
.......... 186
6.
PERMUTATION GROUPS
193
6.1
Multiplication of Permutations
................ 193
6.2
Young Patterns, Young Tableaux and Young Operators
. . 197
6.3
Primitive Idempotents in the Group Algebra
........ 205
6.4
Irreducible Representations and Characters
......... 211
6.5
The Inner and Outer Products of Representations
..... 237
7.
LIE GROUPS AND LIE ALGEBRAS
269
7.1
Classification of
Semisimple
Lie Algebras
.......... 269
7.2
Irreducible Representations and the Chevalley Bases
.... 279
7.3
Reduction of the Direct Product of Representations
.... 299
8.
UNITARY GROUPS
317
8.1
The SU(iV) Group and Its Lie Algebra
............ 317
8.2
Irreducible Tensor Representations of SU(iV)
........ 321
8.3
Orthonormal
Bases for Irreducible Representations
..... 336
8.4
Subduced Representations
................... 362
8.5
Casimir
Invariants of SU(JV)
................ ■ 369
9.
REAL ORTHOGONAL GROUPS
375
9.1
Tensor Representations of SO (JV)
............... 375
9.2
Spinor Representations of SO(iV)
............... 403
9.3
SO(4) Group and the
Lorentz
Group
..........· ■ · 415
10.
THE SYMPLECTIC GROUPS
433
10.1
The Groups Sp(2t,R) and
USp(2ť)
.............. 433
10.2
Irreducible Representations of Sp(2£)
............. 440
Bibliography
457
Index
461
|
| adam_txt |
Contents
Preface
v
1. REVIEW
ON LINEAR ALGEBRAS
1
1.1
Eigenvalues and Eigenvectors of a Matrix
. 1
1.2
Some Special Matrices
. 4
1.3
Similarity Transformation
. 7
2.
GROUP AND ITS SUBSETS
27
2.1
Definition of a Group
. 27
2.2
Subsets in a Group
. 29
2.3
Homomorphism of Groups
. 33
3.
THEORY OF REPRESENTATIONS
43
3.1
Transformation Operators for a Scalar Function
. 43
3.2
Inequivalent and Irreducible Representations
. 47
3.3
Subduced and Induced Representations
. 65
3.4
The Clebsch-Gordan Coefficients
. 79
4.
THREE-DIMENSIONAL ROTATION GROUP
115
4.1
SO(3) Group and Its Covering Group SU(2)
. 115
4.2
Inequivalent and Irreducible Representations
. 123
4.3
Lie Groups and Lie Theorems
. 140
4.4
Irreducible Tensor Operators
. 146
4.5
Unitary Representations with Infinite Dimensions
. 166
5.
SYMMETRY OF CRYSTALS
173
5.1
Symmetric Operations and Space Groups
. 173
χ
Problems
and Solutions in Group Theory
5.2
Symmetric Elements
. 177
5.3
International Notations for Space Groups
. 186
6.
PERMUTATION GROUPS
193
6.1
Multiplication of Permutations
. 193
6.2
Young Patterns, Young Tableaux and Young Operators
. . 197
6.3
Primitive Idempotents in the Group Algebra
. 205
6.4
Irreducible Representations and Characters
. 211
6.5
The Inner and Outer Products of Representations
. 237
7.
LIE GROUPS AND LIE ALGEBRAS
269
7.1
Classification of
Semisimple
Lie Algebras
. 269
7.2
Irreducible Representations and the Chevalley Bases
. 279
7.3
Reduction of the Direct Product of Representations
. 299
8.
UNITARY GROUPS
317
8.1
The SU(iV) Group and Its Lie Algebra
. 317
8.2
Irreducible Tensor Representations of SU(iV)
. 321
8.3
Orthonormal
Bases for Irreducible Representations
. 336
8.4
Subduced Representations
. 362
8.5
Casimir
Invariants of SU(JV)
. ■ 369
9.
REAL ORTHOGONAL GROUPS
375
9.1
Tensor Representations of SO (JV)
. 375
9.2
Spinor Representations of SO(iV)
. 403
9.3
SO(4) Group and the
Lorentz
Group
.· ■ · 415
10.
THE SYMPLECTIC GROUPS
433
10.1
The Groups Sp(2t,R) and
USp(2ť)
. 433
10.2
Irreducible Representations of Sp(2£)
. 440
Bibliography
457
Index
461 |
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| id | DE-604.BV021840588 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:00:18Z |
| indexdate | 2024-07-09T20:45:51Z |
| institution | BVB |
| isbn | 981238832X 9812388338 9789812388339 |
| language | English |
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| physical | X, 464 S. |
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| spelling | Ma, Zhong-Qi 1940- Verfasser (DE-588)131801171 aut Problems & solutions in group theory for physicists Zhong-Qi Ma ; Xiao-Yan Gu Reprint. New Jersey [u.a.] World Scientific 2007 X, 464 S. txt rdacontent n rdamedia nc rdacarrier Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Gruppentheorie (DE-588)4072157-7 s Mathematische Physik (DE-588)4037952-8 s DE-604 Gu, Xiao-Yan Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052450&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ma, Zhong-Qi 1940- Gu, Xiao-Yan Problems & solutions in group theory for physicists Gruppentheorie (DE-588)4072157-7 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4037952-8 (DE-588)4143389-0 |
| title | Problems & solutions in group theory for physicists |
| title_auth | Problems & solutions in group theory for physicists |
| title_exact_search | Problems & solutions in group theory for physicists |
| title_exact_search_txtP | Problems & solutions in group theory for physicists |
| title_full | Problems & solutions in group theory for physicists Zhong-Qi Ma ; Xiao-Yan Gu |
| title_fullStr | Problems & solutions in group theory for physicists Zhong-Qi Ma ; Xiao-Yan Gu |
| title_full_unstemmed | Problems & solutions in group theory for physicists Zhong-Qi Ma ; Xiao-Yan Gu |
| title_short | Problems & solutions in group theory for physicists |
| title_sort | problems solutions in group theory for physicists |
| topic | Gruppentheorie (DE-588)4072157-7 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Gruppentheorie Mathematische Physik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015052450&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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