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“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model. (English) Zbl 1342.81741

Summary: The BPS Skyrme model is a model containing an \(\operatorname{SU}(2)\)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). 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 \(\operatorname{SU}(2)\) 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 exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.{
©2016 American Institute of Physics}

MSC:

81V35 Nuclear physics
81T10 Model quantum field theories
35C08 Soliton solutions
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
22E70 Applications of Lie groups to the sciences; explicit representations
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[1] Skyrme, T. H. R., A nonlinear field theory, Proc. R. Soc. London, Ser. A, 260, 127-138 (1961) · Zbl 0102.22605 · doi:10.1098/rspa.1961.0018
[2] Skyrme, T. H. R., Particle states of a quantized meson field, Proc. R. Soc. London, Ser. A, 262, 237-245 (1961) · Zbl 0099.43605 · doi:10.1098/rspa.1961.0115
[3] Skyrme, T. H. R., A unified field theory of mesons and baryons, Nucl. Phys., 31, 556-569 (1962) · doi:10.1016/0029-5582(62)90775-7
[4] Zahed, I.; Brown, G. E., The Skyrme model, Phys. Rep., 142, 1-102 (1986) · doi:10.1016/0370-1573(86)90142-0
[5] Adam, C.; Sánczhez-Guillén, J.; Wereszczyński, A., A Skyrme-type proposal for baryonic matter, Phys. Lett. B, 691, 105-110 (2010) · doi:10.1016/j.physletb.2010.06.025
[6] Adam, C.; Sánczhez-Guillén, J.; Wereszczyński, A., A BPS Skyrme model—Mathematical properties and physical applications, Acta Phys. Pol., B, 41, 2717 (2010)
[7] Adam, C.; Fosco, C. D.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A., Symmetries and exact solutions of the BPS Skyrme model, J. Phys. A: Math. Theor., 46, 135401 (2013) · Zbl 1266.81128 · doi:10.1088/1751-8113/46/13/135401
[8] Bogomol’nyi, E. B., The stability of classical solutions, Sov. J. Nucl. Phys., 24, 449 (1976)
[9] de Vega, H. J.; Schaposnik, F. A., Classical vortex solution of the Abelian Higgs model, Phys. Rev. D, 14, 1100 (1976) · doi:10.1103/PhysRevD.14.1100
[10] Adam, C.; Sánczhez-Guillén, J.; Wereszczyński, A., BPS Skyrme model and baryons at large \(N_c\), Phys. Rev. D, 82, 085015 (2010) · doi:10.1103/PhysRevD.82.085015
[11] Adam, C.; Naya, C.; Sánczhez-Guillén, J.; Wereszczyński, A., Nuclear binding energies from a Bogomol’nyi-Prasad-Sommerfield Skyrme model, Phys. Rev. C, 88, 054313 (2013) · doi:10.1103/PhysRevC.88.054313
[12] Adam, C.; Naya, C.; Sánchez-Guillén, J.; Vazquez, R.; Wereszczyński, A., BPS skyrmions as neutron stars, Phys. Lett. B, 742, 136-142 (2015) · doi:10.1016/j.physletb.2015.01.027
[13] Adam, C.; Naya, C.; Sánchez-Guillén, J.; Vazquez, R.; Wereszczyński, A., Neutron stars in the Bogomol’nyi-Prasad-Sommerfield Skyrme model: Mean-field limit versus full field theory, Phys. Rev. C, 92, 025802 (2015) · doi:10.1103/PhysRevC.92.025802
[14] Gudnason, S. B.; Nitta, M., Fractional skyrmions and their molecules, Phys. Rev. D, 91, 085040 (2015) · doi:10.1103/PhysRevD.91.085040
[15] Jäykkä, J.; Speight, M.; Sutcliffe, P., Broken baby skyrmions, Proc. R. Soc. London, Ser. A, 468, 1085-1104 (2012) · Zbl 1364.81232 · doi:10.1098/rspa.2011.0543
[16] Kobayashi, M.; Nitta, M., Fractional vortex molecules and vortex polygons in a baby Skyrme model, Phys. Rev. D, 87, 125013 (2013) · doi:10.1103/PhysRevD.87.125013
[17] Kiskis, J., Fermions in a pseudoparticle field, Phys. Rev. D, 15, 2329 (1977) · doi:10.1103/PhysRevD.15.2329
[18] Kiskis, J., U(1) gauge theories, fiber bundles, and stereographic projections in two dimensions, Phys. Rev. D, 16, 2535 (1977) · doi:10.1103/PhysRevD.16.2535
[19] Forgács, P.; Horváth, Z.; Palla, L., Exact, fractionally charged self-dual solution, Phys. Rev. Lett., 46, 392 (1981) · doi:10.1103/PhysRevLett.46.392
[20] Ioannidou, T.; Lukács, Á., Time-dependent Bogomolny-Prasad-Sommerfeld skyrmions, J. Math. Phys., 57, 022901 (2016) · Zbl 1332.81244 · doi:10.1063/1.4940695
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