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

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

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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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