Divergences

Quantum Field Theory · Part 6

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Table of Contents

  1. 1.1.1 The Problem: Infinite Quantum Corrections
  2. 2.1.2 Degree of Divergence: Power Counting
  3. 3.1.3 Examples in φ⁴ Theory
  4. 4.1.4 Divergences in QED
  5. 5.1.5 Subdivergences and Overlapping Divergences
  6. 6.1.6 Renormalizability
  7. 7.1.7 Types of Divergences
  8. 8.(a) Vacuum Bubble
  9. 9.(b) Tadpole (1-point function)
  10. 10.(c) Self-Energy (2-point function)

Key Equations

$$\Pi^{\mu\nu}(q) \sim \int \frac{d^4k}{(2\pi)^4} \frac{\text{Tr}[\gamma^\mu(\gamma \cdot k)\gamma^\nu(\gamma \cdot (k+q))]}{(k^2 - m_e^2)((k+q)^2 - m_e^2)}$$
$$D = 4 - E_B - \frac{3}{2}E_F$$
$$D = 4 - 2 = 2 \quad \text{(quadratic divergence)}$$
$$D = 4 - 2 = 2$$

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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