Group theory for high energy physicists:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton [u.a.]
Taylor & Francis
2013
|
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025391615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 218 S. graph. Darst. |
| ISBN: | 9781466510630 |
Internformat
MARC
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| 100 | 1 | |a Saleem, Mohammad |d 1934- |e Verfasser |0 (DE-588)124082459 |4 aut | |
| 245 | 1 | 0 | |a Group theory for high energy physicists |c Mohammad Saleem ; Muhammad Rafique |
| 264 | 1 | |a Boca Raton [u.a.] |b Taylor & Francis |c 2013 | |
| 300 | |a XI, 218 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Rafique, Muhammad |e Verfasser |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025391615 | |
Datensatz im Suchindex
| _version_ | 1819355496912519168 |
|---|---|
| adam_text | Titel: Group theory for high energy physicists
Autor: Saleem, Mohammad
Jahr: 2013
Contents
Preface......................................................................................................................ix
About the Author...................................................................................................xi
1 Elements of Group Theory...............:...........................................................1
1.1 Definition of a Group............................................................................1
1.2 Some Characteristics of Group Elements..........................................4
1.3 Permutation Groups..............................................................................6
1.4 Multiplication Table............................................................................10
1.5 Subgroups............................................................................................10
1.6 Power of an Element of a Group.......................................................13
1.7 Cyclic Groups.......................................................................................14
1.8 Cosets....................................................................................................16
1.9 Conjugate Elements and Conjugate Classes....................................17
1.10 Conjugate Subgroups..........................................................................17
1.11 Normal Subgroups..............................................................................18
1.12 Center of a Group................................................................................18
1.13 Factor Group........................................................................................19
1.14 Mapping...............................................................................................20
1.15 Homomorphism..................................................................................22
1.16 Kernel....................................................................................................24
1.17 Isomorphism........................................................................................25
1.18 Direct Product of Groups...................................................................27
1.19 Direct Product of Subgroups.............................................................29
2 Group Representations................................................................................31
2.1 Linear Vector Spaces...........................................................................31
2.2 Linearly Independent Vectors...........................................................33
2.3 Basis Vectors........................................................................................33
2.4 Operators..............................................................................................34
2.5 Unitary and Hilbert Vector Spaces...................................................35
2.6 Matrix Representative of a Linear Operator...................................36
2.7 Change of Basis and Matrix Representative of a Linear
Operator................................................................................................40
2.8 Group Representations.......................................................................44
2.9 Equivalent and Unitary Representations........................................47
2.10 Reducible and Irreducible Representations....................................48
2.11 Complex Conjugate and Adjoint Representations.........................49
2.12 Construction of Representations by Addition................................49
2.13 Analysis of Representations..............................................................51
2.14 Irreducible Invariant Subspace.........................................................52
2.15 Matrix Representations and Invariant Subspaces..........................52
2.16 Product Representations....................................................................57
3 Continuous Groups......................................................................................61
3.1 Definition of a Continuous Group....................................................61
3.2 Groups of Linear Transformations...................................................62
3.3 Order of a Group of Transformations..............................................69
3.4 Lie Groups............................................................................................72
3.5 Generators of Lie Groups...................................................................75
3.6 Real Orthogonal Group in Two Dimensions: 0(2).........................84
3.7 Generators of SU(2).............................................................................91
3.8 Generators of SU(3).............................................................................95
3.9 Generators and Parameterization of a Group.................................98
3.10 Matrix Representatives of Generators..............................................99
3.11 Structure Constants..........................................................................101
3.12 Rank of a Lie Group..........................................................................103
3.13 Lie Algebras.......................................................................................104
3.14 Commutation Relations between the Generators of a
Semisimple Lie Group......................................................................105
3.15 Properties of the Roots.....................................................................108
3.16 Structure Constants Na|3...................................................................Ill
3.17 Classification of Simple Groups......................................................112
3.18 Roots of SU(2).....................................................................................114
3.19 Roots of SU(3).....................................................................................115
3.20 Numerical Values of the Structure Constants of SU(3)................122
3.21 Weights of a Representation............................................................122
3.22 Computation of the Highest Weight of Any Irreducible
Representation of SU(3)....................................................................127
3.23 Dimension of any Irreducible Representation of SU(N).............131
3.24 Computation of the Weights of Any Irreducible
Representation of SU(3)....................................................................133
3.25 Weights of Irreducible Representation D8(l,l) of SU(3)................135
3.26 Weight Diagrams..............................................................................138
3.27 Decomposition of a Product of Two Irreducible
Representations.................................................................................139
3.27.1 First Method.........................................................................139
3.27.2 Second Method.....................................................................141
4 Symmetry, Lie Groups, and Physics.......................................................147
4.1 Symmetry...........................................................................................147
4.1.1 Rotational Symmetry..........................................................147
4.1.2 Higher and Lower Symmetries.........................................151
4.1.3 Reflection/Inversion Symmetry........................................151
4.1.4 Concept of Parity..................................................................153
4.1.5 Multiple Symmetries...........................................................155
4.1.6 Combination of Symmetry Operations............................155
4.1.7 Translational Symmetry in Space......................................156
4.1.8 Time-Reversal Symmetry...................................................157
4.1.9 Charge Conjugation.............................................................159
4.1.10 Symmetry Groups and Physics..........................................162
4.2 Casimir Operators.............................................................................165
4.3 Symmetry Group and Unitary Symmetry....................................166
4.4 Symmetry and Physics.....................................................................166
4.5 Group Theory and Elementary Particles.......................................170
Reference.......................................................................................................190
Appendix A.........................................................................................................191
Appendix B..........................................................................................................195
Appendix C.........................................................................................................199
Appendix D.........................................................................................................203
Index.....................................................................................................................207
|
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| illustrated | Illustrated |
| indexdate | 2024-12-20T16:17:24Z |
| institution | BVB |
| isbn | 9781466510630 |
| language | English |
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| spellingShingle | Saleem, Mohammad 1934- Rafique, Muhammad Group theory for high energy physicists |
| title | Group theory for high energy physicists |
| title_auth | Group theory for high energy physicists |
| title_exact_search | Group theory for high energy physicists |
| title_full | Group theory for high energy physicists Mohammad Saleem ; Muhammad Rafique |
| title_fullStr | Group theory for high energy physicists Mohammad Saleem ; Muhammad Rafique |
| title_full_unstemmed | Group theory for high energy physicists Mohammad Saleem ; Muhammad Rafique |
| title_short | Group theory for high energy physicists |
| title_sort | group theory for high energy physicists |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025391615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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