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A concise and authoritative introduction to one of the central theories of modern physics
For a theory as genuinely elegant as the Standard Model—the current framework describing elementary particles and their forces—it can sometimes appear to students to be little more than a complicated collection of particles and ranked list of interactions. The Standard Model in a Nutshell provides a comprehensive and uncommonly accessible introduction to one of the most important subjects in modern physics, revealing why, despite initial appearances, the entire framework really is as elegant as physicists say.
Dave Goldberg uses a "just-in-time" approach to instruction that enables students to gradually develop a deep understanding of the Standard Model even if this is their first exposure to it. He covers everything from relativity, group theory, and relativistic quantum mechanics to the Higgs boson, unification schemes, and physics beyond the Standard Model. The book also looks at new avenues of research that could answer still-unresolved questions and features numerous worked examples, helpful illustrations, and more than 120 exercises.
- Provides an essential introduction to the Standard Model for graduate students and advanced undergraduates across the physical sciences
- Requires no more than an undergraduate-level exposure to quantum mechanics, classical mechanics, and electromagnetism
- Uses a "just-in-time" approach to topics such as group theory, relativity, classical fields, Feynman diagrams, and quantum field theory
- Couched in a conversational tone to make reading and learning easier
- Ideal for a one-semester course or independent study
- Includes a wealth of examples, illustrations, and exercises
- Solutions manual (available only to professors)
Preface for Instructors ix
Acknowledgments xi
Introduction xiii
Table of Symbols xv
1 Special Relativity 1
1.1 Galileo 2
1.2 Vectors and Tensors 3
1.3 Foundations of Relativity 13
1.4 Spacetime 15
1.5 Relativistic Dynamics 19
2 Scalar Fields 24
2.1 The Principle of Least Action 25
2.2 Continuous Fields 29
2.3 The Klein-Gordon Equation 32
2.4 Which Lagrangians Are Allowed? 33
2.5 Complex Scalar Fields 35
3 Noether's Theorem 43
3.1 Conserved Quantities for Particles 44
3.2 Noether's First Theorem 46
3.3 The Stress-Energy Tensor 49
3.4 Angular Momentum 52
3.5 Electric Charge 53
3.6 Digression: Inflation 54
4 Symmetry 61
4.1 What Groups Are 62
4.2 Finite Groups 63
4.3 Lie Groups 66
4.4 SU(2) 70
4.5 SU(3) 74
5 The Dirac Equation 79
5.1 Relativity and Quantum Mechanics 80
5.2 Solutions to the Dirac Equation 86
5.3 The Adjoint Spinor 88
5.4 Coordinate Transformations 90
5.5 Conserved Currents 93
5.6 Discrete Transforms 97
5.7 Quantum Free-Field Theory 100
6 Electromagnetism 109
6.1 A Toy Model of Electromagnetism 109
6.2 Gauge Transformations 112
6.3 Interpreting the Electromagnetic Lagrangian 116
6.4 Solutions to the Classical Free Field 122
6.5 The Low-Energy Limit 123
6.6 Looking Forward 126
7 Quantum Electrodynamics 129
7.1 Particle Decay 130
7.2 Scattering 140
7.3 Feynman Rules for the Toy Scalar Theory 148
7.4 QED 153
8 The Weak Interaction 164
8.1 Leptons 165
8.2 Massive Mediators 168
8.3 SU(2) 171
8.4 Helicity 177
8.5 Feynman Rules for the Weak Interaction 180
9 Electroweak Unification 184
9.1 Leptons and Quarks 184
9.2 Spontaneous Symmetry Breaking 192
9.3 The Higgs Mechanism 195
9.4 Higgs-Fermion Interactions 199
9.5 A Reflection on Free Parameters 202
10 Particle Mixing 205
10.1 Quarks 207
10.2 Neutrinos 216
10.3 Neutrino Masses 222
11 The Strong Interaction 229
11.1 SU(3) 229
11.2 Renormalization 238
11.3 Asymptotic Freedom 245
12 Beyond the Standard Model 253
12.1 Free Parameters 253
12.2 Grand Unified Theories 255
12.3 Supersymmetry 259
12.4 The Strong CP Problem 264
12.5 Some Open Questions 266
Appendix A Spinors and c-Matrices 271
Appendix B Decays and Cross Sections 274
Appendix C Feynman Rules 277
Appendix D Groups 281
Bibliography 283
Index 291
Description
A concise and authoritative introduction to one of the central theories of modern physics
For a theory as genuinely elegant as the Standard Model—the current framework describing elementary particles and their forces—it can sometimes appear to students to be little more than a complicated collection of particles and ranked list of interactions. The Standard Model in a Nutshell provides a comprehensive and uncommonly accessible introduction to one of the most important subjects in modern physics, revealing why, despite initial appearances, the entire framework really is as elegant as physicists say.
Dave Goldberg uses a "just-in-time" approach to instruction that enables students to gradually develop a deep understanding of the Standard Model even if this is their first exposure to it. He covers everything from relativity, group theory, and relativistic quantum mechanics to the Higgs boson, unification schemes, and physics beyond the Standard Model. The book also looks at new avenues of research that could answer still-unresolved questions and features numerous worked examples, helpful illustrations, and more than 120 exercises.
- Provides an essential introduction to the Standard Model for graduate students and advanced undergraduates across the physical sciences
- Requires no more than an undergraduate-level exposure to quantum mechanics, classical mechanics, and electromagnetism
- Uses a "just-in-time" approach to topics such as group theory, relativity, classical fields, Feynman diagrams, and quantum field theory
- Couched in a conversational tone to make reading and learning easier
- Ideal for a one-semester course or independent study
- Includes a wealth of examples, illustrations, and exercises
- Solutions manual (available only to professors)
