The Structure and Interpretation of the Standard Model
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Table of contents
- Cover
- The Structure and Interpretation of the Standard Modeliii
- Copyright pageiv
- Prefacevii
- Contentsix
- Chapter 1. Introduction1
- Chapter 2. Matter Fields13
- 2.1. The local space-time symmetry group13
- 2.2. The configuration space approach21
- 2.3. Curved space-time26
- 2.4. The Wigner approach29
- 2.5. Parity33
- 2.6. Free particles in other universes38
- 2.7. Natural bundles46
- 2.8. Spinor bundles47
- 2.9. Electrons and neutrinos55
- 2.10. Particles and anti-particles57
- 2.11. Fock space and second quantization59
- Chapter 3. Gauge Fields83
- 3.1. Principal fibre bundles and G-structures83
- 3.2. Classification of principal G-bundles85
- 3.3. Gauge connections87
- 3.4. Choice of gauge and gauge transformations89
- 3.5. Gauge field curvature95
- 3.6. The interaction bundle picture99
- Chapter 4. Interactions103
- 4.1. Interacting fields103
- 4.2. Interaction symmetries105
- 4.3. The electroweak gauge connection bundle110
- 4.4. The Higgs field112
- 4.5. Minimal coupling114
- 4.6. The Lagrangian approach120
- 4.7. Quark colours127
- 4.8. Quark mixing and the Cabibbo angle130
- 4.9. The standard model Lagrangian133
- 4.10. Gauge fields in other universes135
- 4.11. Composite systems136
- 4.12. Baryons, mesons and hadron symmetries138
- 4.13. Elementary particles and intrinsic properties143
- Chapter 5. Standard Model Gauge Groups and Representations155
- 5.1. The structure of compact groups157
- 5.2. Standard model irreducible representations158
- 5.3. The standard model gauge group162
- 5.4. Duality and triality167
- 5.5. The electroweak gauge group167
- 5.6. The electromagnetic subgroup169
- Chapter 6. The Standard Model Interacting-Particle Bundle173
- 6.1. Standard model electroweak-unified bundles175
- 6.2. Standard model electroweak-broken bundles182
- Appendices189
- Appendix A. Topology191
- Appendix B. Lie Groups and Lie Algebras195
- Appendix C. Fibre Bundles197
- Appendix D. Representations of SL(2,C) xR3,1 on F(M,Cn)201
- Appendix E. The Method of Induced Representation205
- Appendix F. Canonical Field Quantization209
- Appendix G. Photons and the Gupta-Bleuler Technique211
- Appendix H. Component Expression of the Curvature Two-Form213
- Appendix I. Elementary Particles in String Theory217
- Appendix J. The Structure Theorem for Compact, Connected Lie Groups221
- Appendix K. Irreducible Representations of U(1)225
- Appendix L. Non-Integral Charge and Hypercharge227
- Appendix M. Representations onto Spaces Tensored with C1231
- Appendix N. Electroweak Interaction Bundles233
- Bibliography241
- Further reading245
- Subject Index247
This book provides a philosophically informed and mathematically rigorous introduction to the 'standard model' of particle physics. The standard model is the currently accepted and experimentally verified model of all the particles and interactions in our universe. All the elementary particles in our universe, and all the non-gravitational interactions -the strong nuclear force, the weak nuclear force, and the electromagnetic force - are collected together and, in the case of the weak and electromagnetic forces, unified in the standard model.
Rather than presenting the calculational recipes favored in most treatments of the standard model, this text focuses upon the elegant mathematical structures and the foundational concepts of the standard model.
· Combines an exposition of the philosophical foundations and rigorous mathematical structure of particle physics
· Demonstrates the standard model with elegant mathematics, rather than a medley of computational recipes
· Promotes a group-theoretical and fibre-bundle approach to the standard model, rather than the Lagrangian approach favoured by calculationalists
· Explains the different approaches to particle physics and the standard model which can be found within the literature
Rather than presenting the calculational recipes favored in most treatments of the standard model, this text focuses upon the elegant mathematical structures and the foundational concepts of the standard model.
· Combines an exposition of the philosophical foundations and rigorous mathematical structure of particle physics
· Demonstrates the standard model with elegant mathematics, rather than a medley of computational recipes
· Promotes a group-theoretical and fibre-bundle approach to the standard model, rather than the Lagrangian approach favoured by calculationalists
· Explains the different approaches to particle physics and the standard model which can be found within the literature