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. 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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