Folding in the Skyrme Model

Houghton, C.J. and Krusch, Steffen (2001) Folding in the Skyrme Model. Journal of Mathematical Physics, 42 . pp. 4079-4100. ISSN 0022-2488. (Full text available)

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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
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QC Physics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Steffen Krusch
Date Deposited: 28 Oct 2008 18:56
Last Modified: 25 Jun 2012 14:12
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