Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Low energy dynamics of vibrating Kinks

J. Mateos Guilarte

TL;DR

This work develops a collective coordinates adiabatic framework to describe the low-energy dynamics of Kinks and Kink-AntiKink configurations in the Jackiw-Rebbi model, incorporating both bosonic and fermionic shape modes. By solving the scalar and spinor spectral problems in kink backgrounds, it builds explicit effective Lagrangians for single kinks and kink-antikink pairs, revealing how fermionic fluctuations modify kinetic terms, shift vibrational frequencies, and induce attractive interactions. The analysis uncovers a rich nonintegrable two- and four-dimensional effective dynamics, including fractal-like bion windows and Grassmann-augmented coordinates that reflect fermionic backreaction in a non-supersymmetric setting. The results provide a concrete bridge between microscopic spectral data and macroscopic defect dynamics, with clear avenues for extending to more fields and higher-dimensional solitons such as vortices in gauge theories.

Abstract

Low energy dynamics of Kinks and Kink-AntiKink configurations in the Jackiw-Rebbi model is fully described. The strategy is based in the Collective Coordinates adiabatic approach. The necessary solution of Quantum Mechanical spectral problems, both for scalar and spinorial wave functions, is unveiled as an intermediate step.

Low energy dynamics of vibrating Kinks

TL;DR

This work develops a collective coordinates adiabatic framework to describe the low-energy dynamics of Kinks and Kink-AntiKink configurations in the Jackiw-Rebbi model, incorporating both bosonic and fermionic shape modes. By solving the scalar and spinor spectral problems in kink backgrounds, it builds explicit effective Lagrangians for single kinks and kink-antikink pairs, revealing how fermionic fluctuations modify kinetic terms, shift vibrational frequencies, and induce attractive interactions. The analysis uncovers a rich nonintegrable two- and four-dimensional effective dynamics, including fractal-like bion windows and Grassmann-augmented coordinates that reflect fermionic backreaction in a non-supersymmetric setting. The results provide a concrete bridge between microscopic spectral data and macroscopic defect dynamics, with clear avenues for extending to more fields and higher-dimensional solitons such as vortices in gauge theories.

Abstract

Low energy dynamics of Kinks and Kink-AntiKink configurations in the Jackiw-Rebbi model is fully described. The strategy is based in the Collective Coordinates adiabatic approach. The necessary solution of Quantum Mechanical spectral problems, both for scalar and spinorial wave functions, is unveiled as an intermediate step.
Paper Structure (14 sections, 91 equations, 6 figures)

This paper contains 14 sections, 91 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The Jackiw-Rebbi model in $\mathbb{R}^{1,1}$ Minkowski space-time
  3. Bose/Fermi quanta in homogeneous field backgrounds
  4. Bosonic and Fermionic Kink fluctuations
  5. Higgs bosons propagating over Kink topological defects
  6. Electrons/Positrons propagating over Kink topological defects
  7. Fermionic quanta
  8. Low energy dynamics of vibrating Kinks. Impact of Bosonic and Fermionic shape modes
  9. Low energy dynamics of a single vibrating Kink
  10. Effective dynamics of vibrating Kink-Anti-Kink configurations
  11. Effective kinetic energy
  12. Effective potential energy
  13. Fermionic fluctuations of Kink/Anti-Kink configurations
  14. Outlook

Figures (6)

  • Figure 1: Snapshots of: (left) $g_{aa}[a,-5]$ (center) $g_{aA}[a,5]$ (right) Graphics of $g_{AA}[a]$
  • Figure 2: Tomographic snapshots of the effective potential when the Kink and the Anti-Kink are close to each other for the following amplitudes of the shape mode: $A=0$ (left) $A=1$ (center) $A=3$ (right)
  • Figure 3: 3D graphics of the effective potentialin the $(a,A)$-plane as function of the $(a,A)$-collective coordinates. Interval: $a\in (-2,2)$, $A\in (0,1)$ (left) $a\in (-2,2)$, $A\in(1,2)$ (right) .
  • Figure 4: (left) Graphics of the Kink shape mode and the AntiKink shape mode (right) Graphics of the upper and lower component of the Fermionic shape mode
  • Figure 5: (left) Contribution to the matric of Fermionic fluctuations $G(a)$ as a function of the distance between Kink and Antikink (right) Effective potential $U(a)$ due to Fermionic fluctuations of the Kink/AntiKink configuration also as a function of $a$.
  • ...and 1 more figures