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. 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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