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粒子物理学家用非阿贝尔离散对称导论=aN lntroduction to Non Abelian Discrete Symmetries for Particle Physicists【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】
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- 黄清俊 著
- 出版社:
- ISBN:
- 出版时间:2014
- 标注页数:0页
- 文件大小:28MB
- 文件页数:301页
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图书目录
1 Introduction1
References3
2 Basics of Finite Groups13
References20
3 SN21
3.1 S321
3.1.1 Conjugacy Classes21
3.1.2 Characters and Representations22
3.1.3 Tensor Products22
3.2 S425
3.2.1 Conjugacy Classes27
3.2.2 Characters and Representations27
3.2.3 Tensor Products29
References30
4 AN31
4.1 A431
4.2 A534
4.2.1 Conjugacy Classes35
4.2.2 Characters and Representations35
4.2.3 Tensor Products37
References41
5 T′43
5.1 Conjugacy Classes43
5.2 Characters and Representations44
5.3 Tensor Products47
6 DN51
6.1 DN with N Even51
6.1.1 Conjugacy Classes52
6.1.2 Characters and Representations52
6.1.3 Tensor Products54
6.2 DN with N Odd56
6.2.1 Conjugacy Classes56
6.2.2 Characters and Representations56
6.2.3 Tensor Products57
6.3 D458
6.4 D559
7 QN61
7.1 QN with N=4n61
7.1.1 Conjugacy Classes62
7.1.2 Characters and Representations62
7.1.3 Tensor Products62
7.2 QN with N=4n+264
7.2.1 Conjugacy Classes64
7.2.2 Characters and Representations64
7.2.3 Tensor Products65
7.3 Q466
7.4 Q667
8 QD2N69
8.1 Generic Aspects69
8.1.1 Conjugacy Classes70
8.1.2 Characters and Representations70
8.1.3 Tensor Products71
8.2 QD1672
9 ∑(2N2)75
9.1 Generic Aspects75
9.1.1 Conjugacy Classes75
9.1.2 Characters and Representations76
9.1.3 Tensor Products77
9.2 ∑(18)78
9.3 ∑(32)80
9.4 ∑(50)84
10 △(3N2)87
10.1 △(3N2) with N/3≠Integer87
10.1.1 Conjugacy Classes88
10.1.2 Characters and Representations89
10.1.3 Tensor Products89
10.2 △(3N2) with N/3 Integer91
10.2.1 Conjugacy Classes91
10.2.2 Characters and Representations92
10.2.3 Tensor Products93
10.3 △(27)94
References95
11 TN97
11.1 Generic Aspects97
11.1.1 Conjugacy Classes98
11.1.2 Characters and Representations99
11.1.3 Tensor Products99
11.2 T7100
11.3 T13102
11.4 T19104
References108
12 ∑(3N3)109
12.1 Generic Aspects109
12.1.1 Conjugacy Classes110
12.1.2 Characters and Representations111
12.1.3 Tensor Products112
12.2 ∑(81)113
References121
13 △(6N2)123
13.1 △(6N2)with N/3≠Integer123
13.1.1 Conjugacy Classes123
13.1.2 Characters and Representations126
13.1.3 Tensor Products128
13.2 △(6N2) with N/3 Integer131
13.2.1 Conjugacy Classes131
13.2.2 Characters and Representations133
13.2.3 Tensor Products134
13.3 △(54)138
13.3.1 Conjugacy Classes138
13.3.2 Characters and Representations139
13.3.3 Tensor Products141
References145
14 Subgroups and Decompositions of Multiplets147
14.1 S3147
14.1.1 S3→Z3148
14.1.2 S3→Z2148
14.2 S4149
14.2.1 S4→S3150
14.2.2 S4→A4151
14.2.3 S4→∑(8)151
14.3 A4152
14.3.1 A4→Z3152
14.3.2 A4→Z2×Z2153
14.4 A5153
14.4.1 A5→A4153
14.4.2 A5→D5153
14.4.3 A5→S3?D3154
14.5 T′154
14.5.1 T′→Z6154
14.5.2 T′→Z4155
14.5.3 T′→Q4155
14.6 General DN155
14.6.1 DN→Z2156
14.6.2 DN→ZN157
14.6.3 DN→DM157
14.7 D4158
14.7.1 D4→Z4158
14.7.2 D4→Z2×Z2159
14.7.3 D4→Z2159
14.8 General QN159
14.8.1 QN→Z4160
14.8.2 QN→ZN161
14.8.3 QN→QM161
14.9 Q4162
14.9.1 Q4→Z4162
14.10 QD2N162
14.10.1 QD2N→Z2163
14.10.2 QD2N→ZN163
14.10.3 QD2N→DN/2163
14.11 General∑(2N2)164
14.11.1 ∑(2N2)→Z2N164
14.11.2 ∑(2N2)→ZN×ZN164
14.11.3 ∑(2N2)→DN165
14.11.4 ∑(2N2)→QN166
14.11.5 ∑(2N2)→∑(2M2)166
14.12 ∑(32)167
14.13 General △(3N2)168
14.13.1 △(3N2)→Z3169
14.13.2 △(3N2)→ZN×ZN169
14.13.3 △(3N2)→TN170
14.13.4 △(3N2)→△(3M2)170
14.14 △(27)172
14.14.1 △(27)→Z3172
14.14.2 △(27)→Z3×Z3172
14.15 General TN173
14.15.1 TN→Z3173
14.15.2 TN→ZN173
14.16 T7174
14.16.1 T7→Z3174
14.16.2 T7→Z7175
14.17 General ∑(3N3)175
14.17.1 ∑(3N2)→ZN×ZN×ZN175
14.17.2 ∑(3N3)→△(3N2)175
14.17.3 ∑(3N3)→∑(3M3)176
14.18 ∑(81)176
14.18.1 ∑(81)→Z3×Z3×Z3177
14.18.2 ∑(81)→△(27)177
14.19 General△(6N2)178
14.19.1 △(6N2)→∑(2N2)179
14.19.2 △(6N2)→△(3N2)180
14.19.3 △(6N2)→△(6M2)180
14.20 △(54)181
14.20.1 △(54)→S3×Z3182
14.20.2 △(54)→∑(18)182
14.20.3 △(54)→△(27)183
15 Anomalies185
15.1 Generic Aspects185
15.2 Explicit Calculations189
15.2.1 53189
15.2.2 S4190
15.2.3 A4190
15.2.4 A5191
15.2.5 T′192
15.2.6 DN (N Even)193
15.2.7 DN (N Odd)194
15.2.8 QN(N=4n)194
15.2.9 QN(N=4n+2)195
15.2.10 QD2N196
15.2.11 ∑(2N2)197
15.2.12 △(3N2)(N/3≠Integer)198
15.2.13 △(3N2)(N/3 Integer)199
15.2.14 TN200
15.2.15 ∑(3N3)201
15.2.16 △(6N2)(N/3≠Integer)202
15.2.17 △(6N2)(N/3 Integer)203
15.3 Comments on Anomalies203
References204
16 Non-Abellan Discrete Symmetry in Quark/Lepton Flavor Models205
16.1 Neutrino Flavor Mixing and Neutrino Mass Matrix205
16.2 A4 Flavor Symmetry207
16.2.1 Realizing Tri-Bimaximal Mixing of Flavors207
16.2.2 Breaking Tri-Bimaximal Mixing209
16.3 S4 Flavor Model211
16.4 Alternative Flavor Mixing219
16.5 Comments on Other Applications222
16.6 Comment on Origins of Flavor Symmetries223
References224
Appendix A Useful Theorems229
References235
Appendix B Representations of S4 in Different Bases237
B.1 Basis Ⅰ237
B.2 Basis Ⅱ238
B.3 Basis Ⅲ240
B.4 Basis Ⅳ242
References244
Appendix C Representations of A4 in Different Bases245
C.1 Basis Ⅰ245
C.2 Basis Ⅱ245
References246
Appendix D Representations of A5 in Different Bases247
D.1 Basis Ⅰ247
D.2 Basis Ⅱ253
References259
Appendix E Representations of T'in Different Bases261
E.1 Basis Ⅰ262
E.2 Basis Ⅱ263
References264
Appendix F Other Smaller Groups265
F.1 Z4?Z4265
F.2 Z8?Z2268
F.3 (Z2×Z4)?Z2(Ⅰ)270
F.4 (Z2×Z4)?Z2(Ⅱ)272
F.5 Z3?Z8275
F.6 (Z6×Z2)?Z2277
F.7 Z9?Z3281
References283
Index285
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