Quantum Field Theory

  1. Interacting Fields and Perturbation Theory
    1. Interaction Picture Formalism
      1. Time Evolution Operators
        1. Interaction Picture Definition
          1. Relationship Between Pictures
          2. Separation of Hamiltonians
            1. Free Hamiltonian
              1. Interaction Hamiltonian
                1. Adiabatic Switching
              2. The S-Matrix
                1. Definition and Physical Meaning
                  1. Scattering Operator
                    1. Asymptotic States
                      1. Unitarity
                      2. Perturbative Expansion
                        1. Series in Coupling Constant
                          1. Convergence Issues
                        2. Time-Ordered Products
                          1. Dyson's Formula
                            1. Time-Ordering Operator
                              1. Dyson Series Expansion
                              2. T-Product Properties
                                1. Chronological Ordering
                                  1. Analytic Properties
                                2. Wick's Theorem
                                  1. Normal Ordering
                                    1. Definition for Bosons and Fermions
                                      1. Vacuum Expectation Values
                                      2. Contraction of Operators
                                        1. Wick Contractions
                                          1. Propagator Identification
                                          2. Wick's Theorem Statement
                                            1. Combinatorial Factors
                                              1. Diagrammatic Interpretation
                                            2. Feynman Diagrams
                                              1. Diagrammatic Rules
                                                1. Vertices and Lines
                                                  1. External Lines
                                                    1. Internal Lines
                                                    2. Scalar Field Theory Example
                                                      1. φ⁴ Theory
                                                        1. Interaction Vertex
                                                          1. Propagator Lines
                                                          2. Tree-Level Processes
                                                            1. Loop Corrections
                                                            2. From Diagrams to Amplitudes
                                                              1. Feynman Rules
                                                                1. Momentum Conservation
                                                                  1. Symmetry Factors
                                                                  2. Amplitude Calculation
                                                                    1. Integration over Loop Momenta
                                                                  3. Momentum Space Rules
                                                                    1. Four-Momentum Conservation
                                                                      1. Propagator Factors
                                                                        1. Vertex Factors
                                                                      2. Physical Observables
                                                                        1. Cross Sections
                                                                          1. Differential Cross Sections
                                                                            1. Total Cross Sections
                                                                              1. Optical Theorem
                                                                              2. Decay Rates
                                                                                1. Partial Widths
                                                                                  1. Branching Ratios
                                                                                  2. LSZ Reduction Formula
                                                                                    1. Asymptotic Field Operators
                                                                                      1. Amputated Green's Functions
                                                                                        1. Connection to S-Matrix Elements
                                                                                        2. Phase Space
                                                                                          1. Lorentz-Invariant Phase Space
                                                                                            1. Two-Body Final States
                                                                                              1. Multi-Body Final States
                                                                                                1. Phase Space Integration

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                                                                                            2. Canonical Quantization of Free Fields

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                                                                                            4. Quantum Electrodynamics