## SciPost Submission Page

# An introduction to kinks in $\varphi^4$-theory

### by Mariya Lizunova, Jasper van Wezel

### Submission summary

As Contributors: | Jasper van Wezel |

Arxiv Link: | https://arxiv.org/abs/2009.00355v1 (pdf) |

Date submitted: | 2020-09-02 07:53 |

Submitted by: | van Wezel, Jasper |

Submitted to: | SciPost Physics Lecture Notes |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### Abstract

As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous $\varphi^4$-theory is one of the central models of modern theoretical physics. Its topological defects, or kinks, describe stable, particle-like excitations that play a central role in processes ranging from cosmology to particle physics and condensed matter theory. In these lecture notes, we introduce the description of kinks in $\varphi^4$-theory and the various physical processes that govern their dynamics. The notes are aimed at advanced undergraduate students, and emphasis is placed on stimulating qualitative insight into the rich phenomenology encountered in kink dynamics. The appendices contain more detailed derivations, and allow enquiring students to also obtain a quantitative understanding. Topics covered include the topological classification of stable solutions, kink collisions, the formation of bions, resonant scattering of kinks, and kink-impurity interactions.