Written as a basic introduction to quantum field theory, this book explains the basic physics and formalism behind the theory, covers theory calculations using Feynman diagrams, and introduces the reader to gauge theories, which play such a central role in elementary particle physics. To help students fully understand this subject, mathematical formalism is developed from first principles, its physical interpretation is stressed at every point, and its use is illustrated in detailed applications. Chapters on electroweak interactions have also been reworked and include new material such as Majorana neutrinos.
Table of Contents
Dedication

Preface

1 Photons and the Electromagnetic Field
1.1 Particles and Fields
1.2 The Electromagnetic Field in the Absence of Charges
1.3 The Electric Dipole Interaction
1.4 The Electromagnetic Field in the Presence of Charges
1.5 Appendix: The Schrödinger, Heisenberg and Interaction Pictures

Problems

2 Lagrangian Field Theory
2.1 Relativistic Notation
2.2 Classical Lagrangian Field Theory
2.3 Quantized Lagrangian Field Theory
2.4 Symmetries and Conservation Laws

Problems

3 The Klein–Gordon field
3.1 The Real Klein–Gordon Field
3.2 The Complex Klein–Gordon Field
3.3 Covariant Commutation Relations
3.4 The Meson Propagator

Problems

4 The Dirac Field
4.1 The Number Representation for Fermions
4.2 The Dirac Equation
4.3 Second Quantization
4.4 The Fermion Propagator
4.5 The Electromagnetic Interaction and Gauge Invariance

Problems

5 Photons: Covariant Theory
5.1 The Classical Fields
5.2 Covariant Quantization
5.3 The Photon Propagator

Problems

6 The S-Matrix Expansion
6.1 Natural Dimensions and Units
6.2 The S-Matrix Expansion
6.3 Wick’s Theorem

7 Feynman Diagrams and Rules in QED
7.1 Feynman Diagrams in Configuration Space
7.2 Feynman Diagrams in Momentum Space
7.3 Feynman Rules for QED
7.4 Leptons

Problems

8 QED Processes in Lowest Order
8.1 The Cross-Section
8.2 Spin Sums
8.3 Photon Polarization Sums
8.4 Lepton Pair Production in (eþe_) Collisions
8.5 Bhabha Scattering
8.6 Compton Scattering
8.7 Scattering by an External Field
8.8 Bremsstrahlung
8.9 The Infra-Red Divergence

Problems

9 Radiative Corrections
9.1 The Second-Order Radiative Corrections of QED
9.2 The Photon Self-Energy
9.3 The Electron Self-Energy
9.4 External Line Renormalization
9.5 The Vertex Modification
9.6 Applications
9.7 The Infra-Red Divergence
9.8 Higher-Order Radiative Corrections
9.9 Renomalizability

Problems

10 Regularization
10.1 Mathematical Preliminaries
10.2 Cut-Off Regularization: The Electron Mass Shift
10.3 Dimensional Regularization
10.4 Vacuum Polarization
10.5 The Anomalous Magnetic Moment

Problems

11 Gauge Theories
11.1 The Simplest Gauge Theory: QED
11.2 Quantum Chromodynamics
11.3 Alternative Interactions?
11.4 Appendix: Two Gauge Transformation Results

Problems

12 Field Theory Methods
12.1 Green Functions
12.2 Feynman Diagrams and Feynman Rules
12.3 Relation to S-Matrix Elements
12.4 Functionals and Grassmann Fields
12.5 The Generating Functional

Problems

13 Path Integrals
13.1 Functional Integration
13.2 Path Integrals
13.3 Perturbation Theory
13.4 Gauge Independent Quantization?

Problems

14 Quantum Chromodynamics
14.1 Gluon Fields
14.2 Including Quarks
14.3 Perturbation Theory
14.4 Feynman Rules for QCD
14.5 Renormalizability of QCD

Problems

15 Asymptotic Freedom
15.1 Electron-Positron Annihilation
15.2 The Renormalization Scheme
15.3 The Renormalization Group
15.4 The Strong Coupling Constant
15.5 Applications
15.6 Appendix: Some Loop Diagrams in QCD

Problems

16 Weak Interactions
16.1 Introduction
16.2 Leptonic Weak Interactions
16.3 The Free Vector Boson Field
16.4 The Feynman Rules for the IVB Theory
16.5 Decay Rates
16.6 Applications of the IVB Theory
16.7 Neutrino Masses
16.8 Difficulties with the IVB Theory

Problems

17 A Gauge Theory of Weak Interactions
17.1 QED Revisited
17.2 Global Phase Transformations and Conserved Weak Currents
17.3 The Gauge-Invariant Electro-Weak Interaction
17.4 Properties of the Gauge Bosons
17.5 Lepton and Gauge Boson Masses
18 Spontaneous Symmetry Breaking
18.1 The Goldstone Model
18.2 The Higgs Model
18.3 The Standard Electro-Weak Theory

19 The Standard Electro–weak Theory
19.1 The Lagrangian Density in the Unitary Gauge
19.2 Feynman Rules
19.3 Elastic Neutrino–Electron Scattering
19.4 Electron–Positron Annihilation
19.5 The Higgs Boson

Problems

Appendix A

Appendix B

Index