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

by Mariya Lizunova, Jasper van Wezel

Submission summary

As Contributors: Jasper van Wezel
Arxiv Link: (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


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.

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Submission 2009.00355v1 on 2 September 2020

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