Quantum Field Theory

  1. Non-Abelian Gauge Theories
    1. Mathematical Foundations
      1. Lie Groups and Lie Algebras
        1. Structure Constants
          1. Killing Form
            1. Root Systems
            2. SU(N) Groups
              1. Special Unitary Groups
                1. Generators and Representations
                2. Representations
                  1. Fundamental Representation
                    1. Adjoint Representation
                      1. Tensor Products
                    2. Yang-Mills Theory
                      1. Non-Abelian Gauge Fields
                        1. Gauge Field as Connection
                          1. Parallel Transport
                          2. Field Strength Tensor
                            1. Curvature Tensor
                              1. Non-Abelian Field Strength
                              2. Gauge Transformations
                                1. Local Gauge Transformations
                                  1. Gauge Covariant Derivative
                                  2. Yang-Mills Action
                                    1. Gauge Invariant Action
                                      1. Self-Interactions of Gauge Bosons
                                    2. Quantum Chromodynamics
                                      1. QCD Lagrangian
                                        1. Quark Fields
                                          1. Gluon Fields
                                            1. Color Symmetry
                                            2. Particle Content
                                              1. Quarks
                                                1. Color Charges
                                                  1. Flavor Quantum Numbers
                                                  2. Gluons
                                                    1. Color Octet
                                                      1. Self-Interactions
                                                    2. Feynman Rules for QCD
                                                      1. Quark Propagator
                                                        1. Gluon Propagator
                                                          1. Quark-Gluon Vertex
                                                            1. Three-Gluon Vertex
                                                              1. Four-Gluon Vertex
                                                                1. Ghost Vertices
                                                              2. Properties of QCD
                                                                1. Asymptotic Freedom
                                                                  1. Beta Function Calculation
                                                                    1. Running of Strong Coupling
                                                                      1. Perturbative QCD at High Energy
                                                                      2. Confinement
                                                                        1. Color Singlet States
                                                                          1. Linear Potential
                                                                            1. Wilson Loops
                                                                            2. Chiral Symmetry Breaking
                                                                              1. Quark Condensates
                                                                                1. Hadron Spectrum
                                                                                2. Infrared Behavior
                                                                                  1. Non-Perturbative Effects
                                                                                    1. Lattice QCD

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                                                                                7. Symmetries and Symmetry Breaking

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                                                                                9. The Standard Model