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Folding in the Skyrme Model

Houghton, Conor J, Krusch, Steffen (2001) Folding in the Skyrme Model. Journal of Mathematical Physics, 42 . pp. 4079-4100. ISSN 0022-2488. (doi:10.1063/1.1388199) (KAR id:6107)


There are only three stable singularities of a differentiable map between three-dimensional manifolds, namely folds, cusps and swallowtails. A Skyrme configuration is a map from space to SU(2), and its singularities correspond to the points where the baryon density vanishes. In this paper we consider the singularity structure of Skyrme configurations. The Skyrme model can only be solved numerically. However, there are good analytic ansaetze. The simplest of these, the rational map ansatz, has a non-generic singularity structure. This leads us to introduce a non-holomorphic ansatz as a generalization. For baryon number two, three and four, the approximate solutions derived from this ansatz are closer in energy to the true solutions than any other ansatz solution. We find that there is a tiny amount of negative baryon density for baryon number three, but none for two or four. We comment briefly on the relationship to Bogomolny-Prasad-Sommerfield monopoles.

Item Type: Article
DOI/Identification number: 10.1063/1.1388199
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QC Physics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Steffen Krusch
Date Deposited: 28 Oct 2008 18:56 UTC
Last Modified: 16 Nov 2021 09:44 UTC
Resource URI: (The current URI for this page, for reference purposes)

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