Running Coupling

Quantum Field Theory · Part 6

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Table of Contents

  1. 1.6.1 The Concept of Running
  2. 2.6.2 Running of α in QED
  3. 3.6.3 Running of α_s in QCD
  4. 4.6.4 Two-Loop and Higher-Order Running
  5. 5.6.5 Grand Unification and Coupling Unification
  6. 6.6.6 Threshold Corrections and Decoupling
  7. 7.6.7 Experimental Determination of α_s
  8. 8.The Landau Pole Problem
  9. 9.🌟 Asymptotic Freedom in Action
  10. 10.The QCD Scale Λ_QCD

Key Equations

$$\mu\frac{dg}{d\mu} = \beta(g)$$
$$\int_{\alpha(\mu)}^{\alpha(Q)} \frac{d\alpha'}{\alpha'^2} = \int_\mu^Q \frac{2}{3\pi Q'} dQ'$$
$$Q_{\text{Landau}} \sim m_e e^{3\pi \cdot 137} \sim 10^{286}\text{ GeV}$$
$$\alpha_s(Q^2) = \frac{\alpha_s(\mu^2)}{1 + \frac{\alpha_s(\mu^2)}{2\pi}\beta_0\ln\frac{Q^2}{\mu^2}}$$

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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