Quantum Field Theory

  1. Renormalization Theory
    1. Divergences in Quantum Field Theory
      1. Types of Divergences
        1. Ultraviolet Divergences
          1. High-Energy Behavior
            1. Loop Integration
            2. Infrared Divergences
              1. Low-Energy Behavior
                1. Massless Particle Exchange
              2. Origin of Divergences
                1. Loop Integrals
                  1. Short-Distance Singularities
                2. Regularization Methods
                  1. Cutoff Regularization
                    1. Momentum Cutoff
                      1. Pauli-Villars Regularization
                      2. Dimensional Regularization
                        1. Analytic Continuation in Dimensions
                          1. Minimal Subtraction Scheme
                            1. Modified Minimal Subtraction
                            2. Other Regularization Schemes
                              1. Zeta Function Regularization
                                1. Point-Splitting Regularization
                              2. Renormalization Procedures
                                1. Bare vs Renormalized Parameters
                                  1. Parameter Redefinition
                                    1. Counterterms
                                    2. Counterterm Method
                                      1. Lagrangian with Counterterms
                                        1. Renormalization Conditions
                                        2. BPHZ Renormalization
                                          1. Bogoliubov-Parasiuk-Hepp-Zimmermann
                                            1. Forest Formula
                                              1. Subtraction Schemes
                                            2. Renormalizability Analysis
                                              1. Power Counting
                                                1. Degree of Divergence
                                                  1. Superficial Degree of Divergence
                                                  2. Classification of Theories
                                                    1. Super-renormalizable Theories
                                                      1. Renormalizable Theories
                                                        1. Non-renormalizable Theories
                                                        2. Effective Field Theory Perspective
                                                          1. Relevant and Irrelevant Operators
                                                            1. Operator Dimensions
                                                          2. Renormalization Group
                                                            1. Callan-Symanzik Equation
                                                              1. Beta Functions
                                                                1. Anomalous Dimensions
                                                                2. Running Coupling Constants
                                                                  1. Scale Dependence
                                                                    1. Renormalization Group Flow
                                                                    2. Fixed Points
                                                                      1. Ultraviolet Fixed Points
                                                                        1. Infrared Fixed Points
                                                                          1. Critical Phenomena
                                                                          2. Physical Applications
                                                                            1. Asymptotic Freedom
                                                                              1. Triviality
                                                                                1. Hierarchy Problems