TL;DR
This paper quantitatively analyzes the emergence of the 1-skyrmion on a three-sphere by examining the Hessian spectrum at the identity solution, building on prior qualitative work by N. Manton.
Contribution
It provides a quantitative spectral analysis of the 1-skyrmion formation on a three-sphere, extending previous qualitative approaches.
Findings
Spectrum of the Hessian at the identity solution explains skyrmion appearance.
Quantitative understanding complements prior qualitative analyses.
Method can be applied to similar topological soliton problems.
Abstract
It is shown how the appearance of the 1-skyrmion on the three-sphere of radius L can be understood quantitatively by analyzing spectrum of the Hessian at the identity solution. Previously, this analysis was done qualitatively by N. Manton which used a conformal deformation of the identity solution.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Topological and Geometric Data Analysis · Algebraic and Geometric Analysis