Structure and Interpretation of the Standard Model (eBook)

Gordon McCabe (Autor)

eBook Download: PDF

2011 | 1. Auflage
264 Seiten
Elsevier Science (Verlag)
978-0-08-049830-0 (ISBN)

Infos

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

Inhalt

Cover 1
The Structure and Interpretation of the Standard Model 4
Copyright page 5
Preface 8
Contents 10
Chapter 1. Introduction 14
Chapter 2. Matter Fields 26
2.1. The local space-time symmetry group 26
2.2. The configuration space approach 34
2.3. Curved space-time 39
2.4. The Wigner approach 42
2.5. Parity 46
2.6. Free particles in other universes 51
2.7. Natural bundles 59
2.8. Spinor bundles 60
2.9. Electrons and neutrinos 68
2.10. Particles and anti-particles 70
2.11. Fock space and second quantization 72
Chapter 3. Gauge Fields 96
3.1. Principal fibre bundles and G-structures 96
3.2. Classification of principal G-bundles 98
3.3. Gauge connections 100
3.4. Choice of gauge and gauge transformations 102
3.5. Gauge field curvature 108
3.6. The interaction bundle picture 112
Chapter 4. Interactions 116
4.1. Interacting fields 116
4.2. Interaction symmetries 118
4.3. The electroweak gauge connection bundle 123
4.4. The Higgs field 125
4.5. Minimal coupling 127
4.6. The Lagrangian approach 133
4.7. Quark colours 140
4.8. Quark mixing and the Cabibbo angle 143
4.9. The standard model Lagrangian 146
4.10. Gauge fields in other universes 148
4.11. Composite systems 149
4.12. Baryons, mesons and hadron symmetries 151
4.13. Elementary particles and intrinsic properties 156
Chapter 5. Standard Model Gauge Groups and Representations 168
5.1. The structure of compact groups 170
5.2. Standard model irreducible representations 171
5.3. The standard model gauge group 175
5.4. Duality and triality 180
5.5. The electroweak gauge group 180
5.6. The electromagnetic subgroup 182
Chapter 6. The Standard Model Interacting-Particle Bundle 186
6.1. Standard model electroweak-unified bundles 188
6.2. Standard model electroweak-broken bundles 195
Appendices 202
Appendix A. Topology 204
Appendix B. Lie Groups and Lie Algebras 208
Appendix C. Fibre Bundles 210
Appendix D. Representations of SL(2,C)|xR3,1 on F(M,Cn) 214
Appendix E. The Method of Induced Representation 218
Appendix F. Canonical Field Quantization 222
Appendix G. Photons and the Gupta-Bleuler Technique 224
Appendix H. Component Expression of the Curvature Two-Form 226
Appendix I. Elementary Particles in String Theory 230
Appendix J. The Structure Theorem for Compact, Connected Lie Groups 234
Appendix K. Irreducible Representations of U(1) 238
Appendix L. Non-Integral Charge and Hypercharge 240
Appendix M. Representations onto Spaces Tensored with C1 244
Appendix N. Electroweak Interaction Bundles 246
Bibliography 254
Further reading 258
Subject Index 260

Produkt-Details

• Erscheint lt. Verlag: 30.8.2011
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 0-08-049830-2 / 0080498302
• ISBN-13: 978-0-08-049830-0 / 9780080498300