Renormalization Group

Quantum Field Theory · Part 6

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Table of Contents

  1. 1.5.1 The Renormalization Group Equation
  2. 2.5.2 The Beta Function: Heart of the RG
  3. 3.5.3 Calculating the Beta Function
  4. 4.5.4 Beta Function in QED
  5. 5.5.5 Beta Function in QCD: Asymptotic Freedom
  6. 6.5.6 Callan-Symanzik Equation
  7. 7.5.7 Fixed Points and Critical Behavior
  8. 8.5.8 Wilsonian RG: Integrating Out Modes
  9. 9.5.9 Operator Dimensions and Relevance
  10. 10.5.10 Applications of RG

Key Equations

$$\mu\frac{d}{d\mu}\mathcal{O}(p_i, m(\mu), \lambda(\mu), \mu) = 0$$
$$\gamma_m(\lambda) = \mu\frac{1}{m}\frac{dm}{d\mu}$$
$$\delta\lambda = \frac{3\lambda^2}{16\pi^2\epsilon} + \text{finite}$$
$$\alpha(Q^2) = \frac{\alpha(\mu^2)}{1 - \frac{\alpha(\mu^2)}{3\pi}\ln\frac{Q^2}{\mu^2}}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Field Theory course on CoursesHub.World. A comprehensive graduate-level course in quantum field theory. Covers classical field theory, canonical quantization, path integrals, gauge theories, renormalization, the Standard Model, and advanced ...

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