Solitons

Quantum Field Theory · Part 7

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Table of Contents

  1. 1.3.1 Kinks in (1+1) Dimensions
  2. 2.3.2 Topological Charge of Kinks
  3. 3.3.3 Vortices in (2+1) Dimensions
  4. 4.3.4 Magnetic Monopoles in (3+1) Dimensions
  5. 5.3.5 Dirac Quantization Condition
  6. 6.3.6 Domain Walls
  7. 7.3.7 Cosmic Strings
  8. 8.3.8 Homotopy Groups and Topological Classification
  9. 9.3.9 BPS Bound and Supersymmetry
  10. 10.What is a Soliton?

Key Equations

$$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi - V(\phi)$$
$$Q = \frac{1}{2v}\int_{-\infty}^{\infty} dx \, \partial_x \phi = \frac{1}{2v}[\phi(\infty) - \phi(-\infty)]$$
$$\mathcal{L} = -\frac{1}{4}F_{\mu\nu}^a F^{a,\mu\nu} + \frac{1}{2}(D_\mu \phi)^a(D^\mu \phi)^a - V(\phi)$$
$$V(\phi) = \frac{\lambda}{4}(\phi^2 - v^2)^2$$

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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