Understanding Skyrmions using Rational Maps

Details Understanding Skyrmions using Rational Maps Understanding Skyrmions using Rational Maps

2000-08-14

arxiv.org/abs/hep-th/0008110v2

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 2 figures. To appear in the proceedings of the 3rd European Congress of Mathematics, Barcelona 2000 (Birkhouser)

Scientific paper

We discuss an ansatz for Skyrme fields in three dimensions which uses rational maps between Riemann spheres, and produces shell-like structures of polyhedral form. Houghton, Manton and Sutcliffe showed that a single rational map gives good approximations to the minimal energy Skyrmions up to baryon number of order ten. We show how the method can be generalised by using two or more rational maps to give a double-shell or multi-shell structure. Particularly interesting examples occur at baryon numbers twelve and fourteen.

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