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
