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. 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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