Useful Links
Physics
Quantum Physics
Quantum Field Theory
1. Foundations and Preliminaries
2. Canonical Quantization of Free Fields
3. Interacting Fields and Perturbation Theory
4. Quantum Electrodynamics
5. Renormalization Theory
6. Functional Methods
7. Symmetries and Symmetry Breaking
8. Non-Abelian Gauge Theories
9. The Standard Model
10. Advanced Topics
Renormalization Theory
Divergences in Quantum Field Theory
Types of Divergences
Ultraviolet Divergences
High-Energy Behavior
Loop Integration
Infrared Divergences
Low-Energy Behavior
Massless Particle Exchange
Origin of Divergences
Loop Integrals
Short-Distance Singularities
Regularization Methods
Cutoff Regularization
Momentum Cutoff
Pauli-Villars Regularization
Dimensional Regularization
Analytic Continuation in Dimensions
Minimal Subtraction Scheme
Modified Minimal Subtraction
Other Regularization Schemes
Zeta Function Regularization
Point-Splitting Regularization
Renormalization Procedures
Bare vs Renormalized Parameters
Parameter Redefinition
Counterterms
Counterterm Method
Lagrangian with Counterterms
Renormalization Conditions
BPHZ Renormalization
Bogoliubov-Parasiuk-Hepp-Zimmermann
Forest Formula
Subtraction Schemes
Renormalizability Analysis
Power Counting
Degree of Divergence
Superficial Degree of Divergence
Classification of Theories
Super-renormalizable Theories
Renormalizable Theories
Non-renormalizable Theories
Effective Field Theory Perspective
Relevant and Irrelevant Operators
Operator Dimensions
Renormalization Group
Callan-Symanzik Equation
Beta Functions
Anomalous Dimensions
Running Coupling Constants
Scale Dependence
Renormalization Group Flow
Fixed Points
Ultraviolet Fixed Points
Infrared Fixed Points
Critical Phenomena
Physical Applications
Asymptotic Freedom
Triviality
Hierarchy Problems
Previous
4. Quantum Electrodynamics
Go to top
Next
6. Functional Methods