Quantum Field Theory

Franz Mandl is the author of Quantum Field Theory, 2nd Edition, published by Wiley. Graham Shaw is the author of Quantum Field Theory, 2nd Edition, published by Wiley.

Preface xi Notes xiii 1 Photons and the Electromagnetic Field 1 1.1 Particles and Fields 1 1.2 The Electromagnetic Field in the Absence of Charges 2 1.2.1 The classical field 2 1.2.2 Harmonic oscillator 5 1.2.3 The quantized radiation field 7 1.3 The Electric Dipole Interaction 9 1.4 The Electromagnetic Field in the Presence of Charges 14 1.4.1 Classical electrodynamics 14 1.4.2 Quantum electrodynamics 16 1.4.3 Radiative transitions in atoms 17 1.4.4 Thomson scattering 18 1.5 Appendix: The Schrdinger, Heisenberg and Interaction Pictures 20 Problems 22 2 Lagrangian Field Theory 25 2.1 Relativistic Notation 26 2.2 Classical Lagrangian Field Theory 27 2.3 Quantized Lagrangian Field Theory 30 2.4 Symmetries and Conservation Laws 31 Problems 37 3 The KleinGordon Field 39 3.1 The Real KleinGordon Field 39 3.2 The Complex KleinGordon Field 43 3.3 Covariant Commutation Relations 46 3.4 The Meson Propagator 48 Problems 53 4 The Dirac Field 55 4.1 The Number Representation for Fermions 55 4.2 The Dirac Equation 57 4.3 Second Quantization 61 4.3.1 The spin-statistics theorem 65 4.4 The Fermion Propagator 66 4.5 The Electromagnetic Interaction and Gauge Invariance 70 Problems 71 5 Photons: Covariant Theory 73 5.1 The Classical Fields 73 5.2 Covariant Quantization 77 5.3 The Photon Propagator 81 Problems 84 6 The S-Matrix Expansion 87 6.1 Natural Dimensions and Units 88 6.2 The S-Matrix Expansion 90 6.3 Wicks Theorem 94 7 Feynman Diagrams and Rules in QED 99 7.1 Feynman Diagrams in Configuration Space 100 7.2 Feynman Diagrams in Momentum Space 110 7.2.1 The first-order terms S(1) 112 7.2.2 Compton scattering 113 7.2.3 Electronelectron scattering 116 7.2.4 Closed loops 117 7.3 Feynman Rules for QED 118 7.4 Leptons 121 Problems 124 8 QED Processes in Lowest Order 127 8.1 The Cross-Section 128 8.2 Spin Sums 131 8.3 Photon Polarization Sums 133 8.4 Lepton Pair Production in (e+ e) Collisions 135 8.5 Bhabha Scattering 139 8.6 Compton Scattering 142 8.7 Scattering by an External Field 147 8.8 Bremsstrahlung 153 8.9 The Infrared Divergence 155 Problems 158 9 Radiative Corrections 161 9.1 The Second-Order Radiative Corrections of QED 162 9.2 The Photon Self-Energy 167 9.3 The Electron Self-Energy 172 9.4 External Line Renormalization 176 9.5 The Vertex Modification 178 9.6 Applications 183 9.6.1 The anomalous magnetic moments 183 9.6.2 The Lamb shift 187 9.7 The Infrared Divergence 191 9.8 Higher-Order Radiative Corrections 193 9.9 Renormalizability 198 Problems 200 10 Regularization 203 10.1 Mathematical Preliminaries 204 10.1.1 Some standard integrals 204 10.1.2 Feynman parameterization 205 10.2 Cut-Off Regularization: The Electron Mass Shift 206 10.3 Dimensional Regularization 208 10.3.1 Introduction 208 10.3.2 General results 210 10.4 Vacuum Polarization 211 10.5 The Anomalous Magnetic Moment 214 Problems 217 11 Gauge Theories 219 11.1 The Simplest Gauge Theory: QED 220 11.2 Quantum Chromodynamics 222 11.2.1 Colour and confinement 222 11.2.2 Global phase invariance and colour conservation 225 11.2.3 SU(3) gauge invariance 227 11.2.4 Quantum chromodynamics 229 11.3 Alternative Interactions? 230 11.3.1 Non-minimal interactions 230 11.3.2 Renormalizability 233 11.4 Appendix: Two Gauge Transformation Results 235 11.4.1 The transformation law (11.26b) 236 11.4.2 The SU(3) gauge invariance of Eq. (11.34) 237 Problems 238 12 Field Theory Methods 241 12.1 Green Functions 241 12.2 Feynman Diagrams and Feynman Rules 246 12.2.1 The perturbation expansion 246 12.2.2 The vacuum amplitude 248 12.2.3 The photon propagator 249 12.2.4 Connected Green functions 252 12.3 Relation to S-Matrix Elements 254 12.3.1 Crossing 255 12.4 Functionals and Grassmann Fields 256 12.4.1 Functionals 257 12.4.2 Grassmann algebras and