Regularization

Quantum Field Theory · Part 6

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Table of Contents

  1. 1.2.1 The Need for Regularization
  2. 2.2.2 Momentum Cutoff Regularization
  3. 3.2.3 Pauli-Villars Regularization
  4. 4.2.4 Dimensional Regularization (The Modern Standard)
  5. 5.2.6 Why Dimensional Regularization is Superior
  6. 6.2.7 Lattice Regularization (Brief Mention)
  7. 7.2.8 Comparison of Regularization Schemes
  8. 8.How Dimensional Regularization Works
  9. 9.2.5 Minimal Subtraction (MS) and MS-bar
  10. 10.MS (Minimal Subtraction)

Key Equations

$$I = \int_0^\infty \frac{d^4k}{(2\pi)^4} f(k) \quad \to \quad I_\Lambda = \int_0^\Lambda \frac{d^4k}{(2\pi)^4} f(k)$$
$$\frac{1}{k^2 - m^2} \quad \to \quad \frac{1}{k^2 - m^2} - \sum_i \frac{c_i}{k^2 - M_i^2}$$
$$\int \frac{d^dk}{(2\pi)^d} = \mu^\epsilon \int \frac{d^dk}{(2\pi)^d}$$
$$\Gamma(n - 2 + \epsilon/2) = \Gamma(n-2)\left[1 + \frac{\epsilon}{2}\psi(n-2) + O(\epsilon^2)\right]$$

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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