Table of Contents
Preface ix
Chapter 1 Why Quantum Field Theory? 1
1.1 A successful framework 2
1.2 A universal framework 3
Chapter 2 Quanta 4
2.1 From classical particle mechanics to classical waves: Phonons 4
2.2 From quantum mechanics to Quantum Field Theory 7
2.3 Creation operators and the Hamiltonian 8
2.4 States filled with quanta 11
2.5 Connection with normal modes 14
Chapter 3 Developing free field theory 16
3.1 Quantum mechanics in field theory notation 16
3.2 The infinite-box limit 18
3.3 Relativistic notation, h=c=1, and dimensional analysis 19
3.4 Action principle in general 21
3.5 Energy and momentum 22
3.6 Zero-point energy 24
3.7 Noether's theorem 25
3.8 The relativistic real scalar field 27
3.9 The complex scalar field and antiparticles 28
3.10 The nonrelativistic limit 30
3.11 Photons 31
3.12 Fermions-Preliminary 33
3.13 Why equal-time commutators? 33
Chapter 4 Interactions 36
4.1 Example: Phonons again 36
4.2 Taking matrix elements 38
4.3 Interactions of scalar fields 39
4.4 Dimensional analysis with fields 40
4.5 Some transitions 42
4.6 The Feynman propagator 44
Chapter 5 Feynman rules 49
5.1 The time-development operator 49
5.2 Tree diagrams 52
5.3 Wick's theorem 54
5.4 Loops 55
5.5 Getting rid of disconnected diagrams 59
5.6 The Feynman rules 60
5.7 Quantum Electrodynamics 64
5.8 Relation with old-fashioned perturbation theory 66
Chapter 6 Calculating 71
6.1 Decay rates and cross sections 71
6.2 Some examples 75
6.2.1 Decay rate 75
6.2.2 Cross section 76
6.2.3 Coulomb scattering in scalar Quantum Electrodynamics 76
6.2.4 Coulomb potential 77
6.3 Symmetry breaking 78
6.4 Example: Higgs mechanism and the Meissner effect 83
Chapter 7 Introduction to renormalization 86
7.1 Measurement 86
7.2 Importance of the uncertainty principle 90
7.3 Divergences 91
7.4 Techniques 94
7.5 The renormalization group 96
7.6 Power counting and renormalization 97
7.7 Effective field theory in brief 99
Chapter 8 Path Integrals 104
8.1 Path integrals in quantum mechanics 104
8.2 Path integrals for Quantum Field Theory 107
8.3 The generating functional-Feynman rules again 111
8.4 Connection to statistical physics 116
Chapter 9 A short guide to the rest of the story 119
9.1 Quantizing other fields 119
9.1.1 The Dirac field 120
9.1.2 Gauge bosons 124
9.2 Advanced techniques 127
9.3 Anomalies 128
9.4 Many body field theory 128
9.5 Nonperturbative physics 130
9.6 Bogolyubov coefficients 132
Appendix Calculating loop integrals 135
A.1 Basic techniques 135
A.2 Locality 139
A.3 Unitarity 140
A.4 Passarino-Veltman reduction 141
Bibliography 143
Index 145
