Radiative Corrections

Quantum Field Theory · Part 4

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Table of Contents

  1. 1.6.1 Beyond Tree Level: Loop Diagrams
  2. 2.6.2 UV Divergences and the Need for Regularization
  3. 3.6.3 The Renormalization Program
  4. 4.6.4 The One-Loop Vertex Correction
  5. 5.6.5 Schwinger's Calculation of
  6. 6.Key Concepts (Page 1)

Key Equations

$$\int \frac{d^4k}{(2\pi)^4} \frac{N(k)}{(k^2 - m^2 + i\epsilon)((k-p)^2 - m^2 + i\epsilon)} \sim \int_0^\Lambda \frac{k^3 \, dk}{k^{4-n}} \to \infty$$
$$\psi_0 = \sqrt{Z_2}\,\psi_R, \quad A_0^\mu = \sqrt{Z_3}\,A_R^\mu, \quad m_0 = m + \delta m, \quad e_0 = Z_e \, e$$
$$-ie\Gamma^\mu(p', p) = -ie\gamma^\mu + (-ie)^3 \int \frac{d^4k}{(2\pi)^4} \frac{\gamma^\nu (\not\!k + \not\!p' + m)\gamma^\mu (\not\!k + \not\!p + m)\gamma_\nu}{[(k+p')^2 - m^2][(k+p)^2 - m^2][k^2 - \mu_\gamma^2]}$$
$$F_2(q^2) = \frac{\alpha}{2\pi}\int_0^1 dx\,dy\,dz\;\delta(x+y+z-1)\;\frac{2m^2 z(1-z)}{m^2(1-z)^2 - q^2 xy - \mu_\gamma^2 z}$$

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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