Quantum Field Theory

  1. Canonical Quantization of Free Fields
    1. The Scalar Field
      1. Classical Klein-Gordon Field
        1. Field Equation
          1. Plane Wave Solutions
            1. Normal Modes
            2. Quantization Procedure
              1. Mode Expansion
                1. Positive and Negative Frequency Modes
                  1. Fourier Decomposition
                  2. Canonical Commutation Relations
                    1. Equal-Time Commutators
                      1. Canonical Momentum
                    2. Creation and Annihilation Operators
                      1. Operator Algebra
                        1. Commutation Relations
                          1. Hermiticity Properties
                          2. Physical Interpretation
                            1. Particle Creation and Destruction
                              1. Occupation Number Representation
                            2. Fock Space Construction
                              1. Vacuum State
                                1. Definition and Properties
                                  1. Vacuum Energy
                                  2. Multi-Particle States
                                    1. One-Particle States
                                      1. N-Particle States
                                        1. Symmetrization
                                      2. Field Operator Properties
                                        1. Field Commutation Relations
                                          1. Microcausality
                                            1. Spacelike Separation
                                            2. Time Evolution
                                              1. Heisenberg Picture Fields
                                            3. The Klein-Gordon Propagator
                                              1. Green's Functions
                                                1. Retarded and Advanced Propagators
                                                  1. Feynman Propagator
                                                  2. Causal Structure
                                                    1. Support Properties
                                                      1. Analytic Properties
                                                  3. The Dirac Field
                                                    1. Classical Dirac Theory
                                                      1. Dirac Equation
                                                        1. Relativistic Wave Equation
                                                          1. Covariance Properties
                                                          2. Gamma Matrices
                                                            1. Anticommutation Relations
                                                              1. Representation Theory
                                                              2. Spinor Solutions
                                                                1. Free Particle Solutions
                                                                  1. Helicity States
                                                                2. Plane Wave Solutions
                                                                  1. Positive Energy Solutions
                                                                    1. Particle States
                                                                      1. Spin Projections
                                                                      2. Negative Energy Solutions
                                                                        1. Antiparticle Interpretation
                                                                          1. Charge Conjugation
                                                                        2. Quantization of Dirac Field
                                                                          1. Anticommutation Relations
                                                                            1. Canonical Anticommutators
                                                                              1. Fermi-Dirac Statistics
                                                                              2. Creation and Annihilation Operators
                                                                                1. Fermion Operators
                                                                                  1. Antiparticle Operators
                                                                                2. Fermi-Dirac Statistics
                                                                                  1. Pauli Exclusion Principle
                                                                                    1. Single Occupancy
                                                                                      1. Antisymmetric Wavefunctions
                                                                                      2. Fermi Sea
                                                                                        1. Filled Negative Energy States
                                                                                          1. Normal Ordering
                                                                                        2. The Dirac Propagator
                                                                                          1. Feynman Propagator for Fermions
                                                                                            1. Definition and Properties
                                                                                              1. Momentum Space Form
                                                                                              2. Spectral Representation
                                                                                                1. Positive and Negative Energy Projectors
                                                                                            2. The Electromagnetic Field
                                                                                              1. Classical Maxwell Theory
                                                                                                1. Maxwell Equations
                                                                                                  1. Field Equations in Vacuum
                                                                                                    1. Source Terms
                                                                                                    2. Electromagnetic Potentials
                                                                                                      1. Scalar and Vector Potentials
                                                                                                        1. Gauge Freedom
                                                                                                      2. Quantization Challenges
                                                                                                        1. Gauge Redundancy
                                                                                                          1. Unphysical Degrees of Freedom
                                                                                                            1. Constraint Structure
                                                                                                            2. Negative Norm States
                                                                                                              1. Longitudinal and Scalar Photons
                                                                                                                1. Gupta-Bleuler Problem
                                                                                                              2. Gauge Fixing Procedures
                                                                                                                1. Coulomb Gauge
                                                                                                                  1. Radiation Gauge
                                                                                                                    1. Instantaneous Coulomb Interaction
                                                                                                                    2. Lorentz Gauge
                                                                                                                      1. Covariant Gauge Condition
                                                                                                                        1. Gauge Parameter
                                                                                                                      2. Gupta-Bleuler Quantization
                                                                                                                        1. Physical State Condition
                                                                                                                          1. Subsidiary Condition
                                                                                                                            1. BRST Cohomology
                                                                                                                            2. Indefinite Metric
                                                                                                                              1. Krein Space
                                                                                                                                1. Positive Definite Subspace
                                                                                                                              2. Physical Photon States
                                                                                                                                1. Polarization Vectors
                                                                                                                                  1. Transverse Polarizations
                                                                                                                                    1. Helicity States
                                                                                                                                    2. Transverse Modes
                                                                                                                                      1. Physical Degrees of Freedom
                                                                                                                                        1. Massless Vector Particles
                                                                                                                                      2. The Photon Propagator
                                                                                                                                        1. Feynman Gauge
                                                                                                                                          1. Covariant Form
                                                                                                                                            1. Gauge Parameter Choice
                                                                                                                                            2. Covariant Propagator
                                                                                                                                              1. Momentum Space Expression
                                                                                                                                                1. Pole Structure

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                                                                                                                                          1. Foundations and Preliminaries

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                                                                                                                                          3. Interacting Fields and Perturbation Theory