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. Free online course in Quantum Field Theory (QFT). 8 parts covering classical field theory, canonical quantization, path integrals, QED, non-Abelian gauge theories, renormalization, the Standard Model,...

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