1 Special Relativity 1.1 The Principle of Relativity 1.1.1 Galilean Relativity in Classical Mechanics 1.1.2 Invariance of Classical Mechanics Under Galilean Transformations 1.2 The Speed of Light and Electromagnetism 1.3 Lorentz Transformations 1.4 Kinematic Consequences of the Lorentz Transformations 1.5 Ptoper Time and Space—Time Diagrams 1.5.1 Space—Time and Causality 1.6 Composition of Velocities 1.6.1 Aberration Revisited 1.7 Experimental Tests of Special Relativity Reference 2 Relativistic Dynamics 2.1 Relativistic Energy and Momentum 2.1.1 Energy and Mass 2.1.2 Nuclear Fusion and the Energy of a Star 2.2 Space—Time and Four—Vectors 2.2.1 Four—Vectors 2.2.2 Relativistic Theories and Poincare Transformations Reference 3 The Equivalence Principle 3.1 Inertial and Gravitational Masses 3.2 Tidal Forces 3.3 The Geometric Analogy 3.4 Curvature 3.4.1 An Elementary Approach to the Curvature 3.4.2 Parallel Transport 3.4.3 Tidal Forces and Space—Time Curvature 3.5 Motion of a Particle in Curved Space—Time 3.5.1 The Newtonian Limit 3.5.2 Time Intervals in a Gravitational Field 3.5.3 The Einstein Equation Reference 4 The Poincare Group 4.1 Linear Vector Spaces 4.1.1 Covariant and Contravariant Components 4.2 Tensors 4.3 Tensor Algebra 4.4 Rotations in Three—Dimensions 4.5 Groups of Transformations 4.5.1 Lie Algebra of the SO（3） Group 4.6 Principle of Relativity and Covariance of Physical Laws 4.7 Minkowski Space—Time and Lorentz Transformations 4.7.1 General Form of （Proper） Lorentz Transformations 4.7.2 The Poincare Group Reference 5 Maxwell Equations and Special Relahvity 5.1 Electromagnetism in Tensor Form 5.2 The Lorentz Force
5.3 Behavior of E and B Under Lorentz Transformations 5.4 The Four—Current and the Conservation of the Electric Charge 5.5 The Energy—Momentum Tensor 5.6 The Four—Potential 5.6.1 The Spin of a Plane Wave 5.6.2 Large Volume Limit Reference 6 Quantization of the Electromagnetic Field 6.1 The Electromagnetic Field as an Infinite System of Harmonic Oscillators 6.2 Quantization of the Electromagnetic Field 6.3 Spin of the Photon Reference 7 Group Representations and Lie Algebras 7.1 Lie Groups 7.2 Representations 7.3 Infinitesimal Transformations and Lie Algebras 7.4 Representation of a Group on a Field 7.4.1 Invariance of Fields 7.4.2 Infinitesimal Transformations on Fields 7.4.3 Application to Non—Relativistic Quantum Mechanics Reference 8 Lagrangian and Hamiltonian Formalism 8.1 Dynamical System with a Finite Number of Degrees of Freedom 8.1.1 The Action Principle 8.1.2 Lagrangian of a Relativistic Particle 8.2 Conservation Laws 8.2.1 The Noether Theorem for a System of Particles 8.3 The Hamiltonian Formalism 8.4 Canonical Transformations and Conserved Quantities 8.4.1 Conservation Laws in the Hamiltonian Formalism 8.5 Lagrangian and Hamiltonian Formalism in Field Theories 8.5.1 Functional Derivative 8.5.2 The Hamilton Principle of Stationary Action 8.6 The Action of the Electromagnetic Field 8.6.1 The Hamiltonian for an Interacting Charge 8.7 Symmetry and the Noether Theorem 8.8 Space—Time Symmetries 8.8.1 Internal Symmetries 8.9 Hamiltonian Formalism in Field Theory 8.9.1 Symmetry Generators in Field Theories Reference 9 Quantum Mechanics Formalism 9.1 Introduction 9.2 Wave Functions， Quantum States and Linear Operators 9.3 Unitary Operators 9.3.1 Application to Non—Relativistic Quantum Theory 9.3.2 The Time Evolution Operator 9.4 Towards a Relativistically Covariant Description 9.4.1 The Momentum Representation 9.4.2 Particles and Irreducible Representations of the Poincare Group
9.5 A Note on Lorentz Invariant Normalizations Reference 10 Relativistic Wave Equations 10.1 The Relativistic Wave Equation 10.2 The Klein—Gordon Equation 10.2.1 Coupling of the Complex Scalar Field φ（x） to the Electromagnetic Field 10.3 The Hamiltonian Formalism for the Free Scalar Field 10.4 The Dirac Equation 10.4.1 The Wave Equation for Spin 1／2 Particles 10.4.2 Conservation of Probability 10.4.3 Covariance of the Dirac Equation 10.4.4 Infinitesimal Generators and Angular Momentum 10.5 Lagrangian and Hamiltonian Formalism 10.6 Plane Wave Solutions to the Dirac Equation 10.6.1 Useful Properties of the u（p， r） and v（p， r） Spinors 10.6.2 Charge Conjugation 10.6.3 Spin Projectors 10.7 Dirac Equation in an External Electromagnetic Field 10.8 Parity Transformation and Bilinear Forms 10.8.1 Bilinear Forms Reference 11 Quantu：ation of Boson and Fermion Fields 11.1 Introduction 11.2 Quantization of the Klein—Gordon Field 11.2.1 Electric Charge and its Conservation 11.3 Transformation Under the Poincare Group 11.3.1 Discrete Transformations 11.4 Invariant Commutation Rules and Causality 11.4.1 Green's Functions and the Feynman Propagator 11.5 Quantization of the Dirac Field 11.6 Invariant Commutation Rules for the Dirac Field 11.6.1 The Feynman P；ropagator for Ferrruons 11.6.2 Transformation Properties of the Dirac Quantum Field 11.6.3 Discrete Transformations 11.7 Covariant Quantization of the Electromagnetic Field 11.7.1 Indefinite Metric and Subsidiary Conditions 11.7.2 Poincare Transformations and Discrete Symmetries 11.8 Quantum Electrodynamics Reference 12 Fields in Interaction 12.1 Interaction Processes 12.2 Kinematics of Interaction Processes 12.2.1 Decay Processes 12.2.2 Scattering Processes 12.3 Dynamics of Interaction Processes 12.3.1 Interaction Representation 12.3.2 The Scattering Matrix 12.3.3 Two-Particle Phase-Space Element 12.3.4 The Optical Theorem 12.3.5 Natural Units
12.3.6 The Wick's Theorem 12.4 Quantum Electrodynamics and Feynman Rules 12.4.1 External Electromagnetic Field 12.5 Amplitudes in the Momentum Representation 12.5.1 M611er Scattering 12.5.2 A Comment on the Role of Virtual Photons 12.5.3 Bhabha and Electron-Muon Scattering 12.5.4 Compton Scattering and Feynrnan Rules 12.5.5 Gauge Invariance of Amplitudes 12.5.6 Interaction with an External Field 12.6 Cross Sections 12.6.1 The Bahbha Scattering 12.6.2 The Compton Scattering 12.7 Divergent Diagrams 12.8 A Pedagogical Introduction to Renormalization 12.8.1 Power Counting and Renormalizability 12.8.2 The Electron Self-Energy Part 12.8.3 The Photon Self-Energy 12.8.4 The Vertex Part 12.8.5 One-Loop Renormalized Lagrangian 12.8.6 The Electron Anomalous Magnetic Moment Reference Appendix A: The Eotvos' Experiment Appendix B: The Newtonian Limit of the Geodesic Equation Appendix C: The Twin Paradox Appendix D: Jacobi Identity for Poisson Brackets Appendix E: Induced Representations and Little Groups Appendix F: SU(2) and SO(3) Appendix G: Gamma Matrix Identifies References Index
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