An introduction to kinks in ${\phi }^4$-theory

Abstract

As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous ${\phi }^4$-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 ${\phi }^4$-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.

arXiv comment27 pages, submitted to SciPost Physics Lecture Notes; small updates

References in corpus (26)

• Kink-antikink collisions in the phi^6 model
• An Introduction to Spontaneous Symmetry Breaking
• Deformed Defects
• Oscillons and Quasi-breathers in the ϕ^4 Klein-Gordon model
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins
• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Small amplitude quasi-breathers and oscillons
• Domain Walls as Dark Energy
• Kink excitation spectra in the (1+1)-dimensional ${\phi }^8$ model
• Kink-Antikink Scattering in ϕ^4 and ϕ^6 Models
• Reflection, transmutation, annihilation and resonance in two-component kink collisions
• Resonance structures in coupled two-component ${\varphi }^4$ model
• Fermionic Zero Modes on Domain Walls
• Kinks and antikinks of buckled graphene: A testing ground for phi^4 field model
• Dark soliton past a finite-size obstacle
• High energy density in the collision of $N$ kinks in the ${\varphi }^4$ model
• Analytical formulation for soliton-potential dynamics
• Chaotic scattering in solitary wave interactions: A singular iterated-map description
• Towards Quantitative Classification of Folded Proteins in Terms of Elementary Functions
• Kink-antikink asymmetry and impurity interactions in topological mechanical chains
• Kink nucleation in two-dimensional Frenkel-Kontorova model
• Gauge symmetries and structure of proteins
• Kink-Antikink Formation from an Oscillation Mode by Sudden Distortion of the Evolution Potential
• Kink Dynamics in a Topological Phi^4 Lattice
• Search for long-living topological solutions of nonlinear ${\phi }^4$ field theory

Cited by in corpus (3)

• Two-Loop Scalar Kinks
• Resonance structures in kink-antikink scattering in a quantum vacuum
• Leading Quantum Correction to the ${\Phi }^4$ Kink Form Factor