TL;DR
This paper analyzes the properties of Skyrmion solutions on a three-cylinder, providing an exact analytic form, energy calculation, and stability analysis, and concludes the uniqueness of such solutions in this setting.
Contribution
It presents the first exact analytic shape function for a 1-Skyrmion on a three-cylinder and analyzes its stability and energy, establishing uniqueness of solutions.
Findings
Exact analytic shape function expressed via elliptic integrals
Calculated energy of the 1-Skyrmion
Proved no other topologically nontrivial solutions exist on the three-cylinder
Abstract
The class of static, spherically symmetric, and finite energy hedgehog solutions in the SU(2) Skyrme model is examined on a metric three-cylinder. The exact analytic shape function of the 1-Skyrmion is found. It can be expressed via elliptic integrals. Its energy is calculated, and its stability with respect to radial and spherically symmetric deformations is analyzed. No other topologically nontrivial solutions belonging to this class are possible on the three-cylinder.
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Taxonomy
TopicsAncient Mediterranean Archaeology and History