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"Half a proton" in the Bogomol'nyi-Prasad-Sommerfield Skyrme model

Abstract

The BPS Skyrme model is a model containing an SU(2)SU(2)-valued scalar field, in which a Bogomol'nyi-type inequality can be satisfied by soliton solutions. In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU(2)SU(2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here, that in the BPS Skyrme model such solutions exists, that a fraction of their charge and energy densities are localised, and the remaining part can be any far away, not interacting with the localised part.Comment: 5 pages, no figures; updated to final versio

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