Instantons

Quantum Field Theory · Part 7

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Table of Contents

  1. 1.2.1 Path Integral in Euclidean Time
  2. 2.2.2 Example: Double-Well Potential
  3. 3.2.3 Instantons in Yang-Mills Theory
  4. 4.2.4 The BPST Instanton
  5. 5.2.5 Topological Charge and Pontryagin Index
  6. 6.2.6 Theta Vacua and the Strong CP Problem
  7. 7.2.7 The Axion Solution
  8. 8.2.8 Physical Effects of Instantons
  9. 9.2.9 Semiclassical Approximation
  10. 10.What is an Instanton?

Key Equations

$$\langle q_f, t_f | q_i, t_i \rangle = \int \mathcal{D}q(t) \, e^{iS[q]}$$
$$S_E[\text{instanton}] = \frac{4ma^3\omega}{3\sqrt{2}}$$
$$A_\mu^a(x) = \frac{2\eta_{\mu\nu}^a (x-x_0)_\nu}{(x-x_0)^2 + \rho^2}$$
$$\mathcal{L}_\theta = \frac{\theta g^2}{32\pi^2} F_{\mu\nu}^a \tilde{F}^{a,\mu\nu}$$

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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