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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】

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
  • 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
  • 主题词:

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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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