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. 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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