Counterterms

Quantum Field Theory · Part 6

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Table of Contents

  1. 1.3.1 Bare vs. Renormalized Parameters
  2. 2.3.2 Example: φ⁴ Theory
  3. 3.3.3 One-Loop Renormalization of φ⁴
  4. 4.3.4 Counterterms in QED
  5. 5.3.5 Ward Identity and Charge Renormalization
  6. 6.3.6 Systematic Renormalization: BPHZ
  7. 7.3.7 Physical Interpretation
  8. 8.(a) Tadpole Diagram
  9. 9.(b) Self-Energy
  10. 10.(c) Vertex Correction

Key Equations

$$\mathcal{L} = \frac{1}{2}(\partial_\mu\phi_0)^2 - \frac{1}{2}m_0^2\phi_0^2 - \frac{\lambda_0}{4!}\phi_0^4$$
$$T = -\frac{i\lambda}{2} \int \frac{d^dk}{(2\pi)^d} \frac{1}{k^2 - m^2} = -\frac{\lambda m^2}{32\pi^2}\left(\frac{2}{\epsilon} - \ln\frac{m^2}{\mu^2} + \text{finite}\right)$$
$$\delta\lambda = \frac{3\lambda^2}{16\pi^2\epsilon} + \text{finite}$$
$$\delta Z_2 = -\frac{e^2}{8\pi^2\epsilon} + \text{finite}$$

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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