Relativistic quantum mechanics and quantum field theory

This book deals with the single particle relativistic wave equations and the elements of quantum field theory. The Klein-Gordon equation is discussed briefly and elaborately the Dirac equation, its free particle solutions and Feynman's positron theory with a view to emphasize how the intuitive approach of Feynman has enormously simplified the calculations in Quantum Electrodynamics the interaction of radiation with matter by the introduction of Feynman diagrams. It is shown that Feynman's approach is equivalent to the other more general approach of quantum field theory and the equivalence of the two approaches has been demonstrated through the S-matrix formalism which leads to the Feynman diagrams by the application of Wick's theorem. How the quantum field theory is stretched beyond quantum electrodynamics to include electro weak interactions and strong interactions and how it leads to the formulation of the standard model of elementary particles are briefly discussed. Table of Contents Preface Introduction The Dirac Equation and its Solutions The Propagation Kernel and Feynman Diagrams Quantum Electrodynamics Radiative Corrections Elements of Quantum Field Theory The Scalar Fields The Dirac Field The Electromagnetic Field Interaction between Fields Recent Developments Appendix List of Symbols and Notation Appendix The Density of Final States Bibliography Subject Index. Preface 8 Contents 12 1 Introduction 17 1.1 The Schr odinger Equation 18 1.2 The Klein-Gordon Equation 19 1.3 The Dirac Equation 21 1.5 Quantum Electrodynamics 28 1.6 Quantum Field Theory 29 2 The Dirac Equation and its Solutions 37 2.1 The free particle solutions 37 2.2 Orthogonal and Closure Properties 40 2.3 Projection Operators 42 2.4 Sum over Spin States 42 2.5 In Feynman's Notation 43 2.6 A Consistency Check 50 2.7 Algebra of Matrices 51 3 The Propagation Kernel and Feynman Diagrams 60 3.1 The Propagation Kernel 60 3.2 The Transition Amplitude 67 3.3 Feynman Diagrams 69 4 Quantum Electrodynamics 76 4.1 Rutherford Scattering 76 4.2 Compton Scattering 81 4.3 Electron-electron Scattering 90 4.4 Electron-positron Scattering 96 4.5 Electron-positron Pair Annihilation into two Photons 99 4.6 Bremsstrahlung 103 5 Radiative Corrections 125 5.1 Electron Self Energy 125 5.2 Higher Order Corrections 130 6 Elements of Quantum Field Theory 139 6.1 A Brief Review of Classical Mechanics 140 6.2 Quantization of the Field 145 6.3 Relativistic Fields 151 7 The Scalar Fields 158 7.1 One-component Real Field 158 7.2 Complex Scalar Field 164 7.3 The Covariant Commutation Relations 169 8 The Dirac Field 179 8.1 Plane Wave Solutions of the Dirac Equation 180 8.2 Lagrangian Density for the Dirac Field 182 8.3 Fourier Decomposition of the Dirac Field 183 8.4 Quantization of the Dirac Field 185 8.5 Covariant Anticommutation Relations 188 9 The Electromagnetic Field 195 9.1 Maxwell's Equations 196 9.2 Electromagnetic Field Tensor 199 9.3 Quantization of the Electromagnetic Field 202 9.4 The Gupta-Bleuler Formulation 204 10 Interaction between Fields 213 10.1 The Tomonaga-Schwinger Equation 214 10.2 The Invariant Perturbation Theory 215 10.3 The S-matrix 218 10.4 Reduction of the S-matrix 219 10.5 From S-matrix Expansion to Feynman diagrams 225 11 Recent Developments 235 11.1 The Renormalization Program 235 11.2 Gauge Theories 237 11.3 The Standard Model 244 11.4 Gravitational Interaction 249 11.5 Birth of String Theory 250 11.6 Superstring Theories 254 Appendix A List of Symbols and Notation 259 Appendix B The Density of Final States 264 Bibliography 266 Subject Index 269 Relativistic,Quantum,Mechanics,and,Quantum,Field,Theory