Contents
Preface
xiii
I Introductory Survey, Electromagnetism as a Gauge
Theory, and Relativistic Quantum Mechanics
1
1 The Particles and Forces of the Standard Model
3
1.1 Introduction: the Standard Model . . . . . . . . . . . . . . .
3

1.2 The fermions of the Standard Model . . . . . . . . . . . . . .
4
1.2.1 Leptons . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.2 Quarks . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.3 Particle interactions in the Standard Model . . . . . . . . . .
12

1.3.1 Classical and quantum fields . . . . . . . . . . . . . .
12
1.3.2 The Yukawa theory of force as virtual quantum exchange . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
1.3.3 The one-quantum exchange amplitude . . . . . . . . .
19

1.3.4 Electromagnetic interactions . . . . . . . . . . . . . .
21
1.3.5 Weak interactions . . . . . . . . . . . . . . . . . . . .
22
1.3.6 Strong interactions . . . . . . . . . . . . . . . . . . . .
26
1.3.7 The gauge bosons of the Standard Model . . . . . . .
29

1.4 Renormalization and the Higgs sector of the Standard Model
30

1.4.1 Renormalization . . . . . . . . . . . . . . . . . . . . .
30
1.4.2 The Higgs boson of the Standard Model . . . . . . . .
33

1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2 Electromagnetism as a Gauge Theory
41
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.2 The Maxwell equations: current conservation . . . . . . . . .
43
2.3 The Maxwell equations: Lorentz covariance and gauge invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
2.4 Gauge invariance (and covariance) in quantum mechanics . .
49

2.5 The argument reversed: the gauge principle . . . . . . . . . .
52

2.6 Comments on the gauge principle in electromagnetism . . . .
56

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
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