CONTENTS
Chapter 1. INTRODUCING QUANTUM FIELDS The Classical String The Quantum String Second Quantization Creation and Annihilation Operators Bose and Fermi Statistics Problems Chapter 2. SCALAR FIELDS Klein-Gordon Equation Real Scalar Field Energy and Momentum Particle Spectrum Continuum Normalization Complex Scalar Field Charge and Antiparticle Microcausality The Feynman Propagator The Wave Functional Functional Operations Vacuum Wave Functional The Phi4 Theory Problems Chapter 3. RELATIVISTIC FIELDS Lorentz Transformations Minimal Representation: SLChapter 2C) The Poincare Group Scalar, Vector, and Spinor Fields Relativistic Quantum Fields One-Particle States Problems Chapter 4. CANONICAL FORMALISM Principle of Stationary Action Noether's Theorem Translational Invariance Lorentz Invariance Symmetrized Energy-Momentum Tensor Gauge Invariance Problems Chapter 5. ELECTROMAGNETIC FIELD Maxwell's Equations Covariance of the Classical Theory Canonical Formalism Quantization in Coulomb Gauge Spin Angular Momentum Intrinsic Parity Transverse Propagator Vacuum Fluctuations The Casimir Effect The Gauge Principle Problems Chapter 6. Dirac Equation Dirac Algebra Wave Functions and Current Density Plane Waves Lorentz Transformations Interpretation of Dirac Matrices External Electromagnetic field Non-Relativistic Limit Thomas Precession Hole Theory Charge Conjugation Massless Particles Problems Chapter 7. The Dirac Field Quantization of the Dirac Field Feynman Propagator Normal Ordering Electromagnetic Interactions Isospin Parity Charge Conjugation Time Reversal Problems Chapter 8. Dynamics of Interacting Fields Time Evolution Interaction Picture Adiabatic Switching Correlation Functions in the Interaction Picture S-Matrix and Scattering Scattering Cross Section Potential Scattering Adiabatic Theorem Problems Chapter 9. Feynman Graphs Perturbation Theory Time-Ordered and Normal Products Wick's Theorem Feynman Rules for Scalar Theory Types of Feynman Graphs Wick Rotation Regularization Schemes Problems Chapter 10. Vacuum Correlation Functions Feynman Rules Reduction Formula The Generating Functional Connected Correlation Functions Lehmann Representation Dyson-Schwinger Equations Bound States Bethe-Salpeter Equation Problems Chapter 11. Quantum Electrodynamics Interaction Hamiltonian Photon Propagator Feynman Graphs Feynman Rules Properties of Feynman Graphs Problems Chapter 12. Processes in Quantum Electrodynamics Compton Scattering Electromagnetic Form Factors Anomalous Magnetic Moment Charge Distribution Problems Chapter 13. Perturbative Renormalization Primitive Divergences in QED Electron Self-Energy Vacuum Polarization Running Coupling Constant Full Vertex Ward Identity Renormalization to Second Order Renormalization to All Orders Callan-Symanzik Equation Triviality Problems Chapter 14. PATH INTEGRALS Path integrals in Quantum Mechanics Imaginary Time Path Integrals in Quantum Field Theory Euclidean Space-time Vacuum Amplitudes Statistical Mechanics Gaussian Integrals Perturbation Theory The Loop Expansion Boson and Fermion Loops Grassmann Variables Problems Chapter 15. Broken Symmetry Why Broken Symmetry Ferromagnetism Spin Waves Breaking Gauge Invariance Superfluidity Ginsburg-Landau Theory Effective Action Effective Potential Problems Chapter 16. Renormalization The Cutoff as Scale Parameter Momentum Space RG Real Space RG Renormalization of Correlation Functions Relevant and Irrelevant Parameters The Free Field IR Fixed Point and Phase Transition Crossover Relation with Perturbative Renormalization Why Correct Theories are Beautiful Problems Chapter 17. The Gaussian Fixed Point Stability of the Free Field General Scalar Field Feynman Graphs Wegner-Houghton Formula Renormalized Couplings The RG Matrix Non-Triviality and Asymptotic Freedom The Case d=2 Problems Chapter 18. In Two Dimensions Absence of Long-Range Order Topological Order XY Model Kosterlitz-Thouless Transition Vortex Model 2D Superfluidity RG Trajectories Universal Jump of Superfluid Density Problems Chapter 19. Topological Excitations Topological Soliton Instanton and Tunneling Depinning of Charge Density Waves Nonlinear Sigma Model The Skyrmion The Hopf Invariant Fractional Spin Monopoles, Vortices, and Anomalies Problems Appendix A. Background Material Notation Classical Mechanics Quantum Mechanics Appendix B. Linear Response