The Standard Model in a Nutshell

The Standard Model in a Nutshell

by Dave Goldberg

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Overview

The Standard Model in a Nutshell by Dave Goldberg

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)

Product Details

ISBN-13: 9780691167596
Publisher: Princeton University Press
Publication date: 02/28/2017
Series: In a Nutshell
Pages: 320
Sales rank: 548,880
Product dimensions: 7.20(w) x 10.00(h) x 1.00(d)

About the Author

Dave Goldberg is professor of physics at Drexel University, where he also serves as associate dean for research and graduate studies at the College of Arts and Sciences. He is the author of The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality and the coauthor of A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty.

Table of Contents

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

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