Magnetic zero-modes, vortices and Cartan geometry

We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the roun...

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Detalles Bibliográficos
Autores principales: Ross, Calum, Schroers, Bernd J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5869901/
https://www.ncbi.nlm.nih.gov/pubmed/29606790
http://dx.doi.org/10.1007/s11005-017-1023-2
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author Ross, Calum
Schroers, Bernd J.
author_facet Ross, Calum
Schroers, Bernd J.
author_sort Ross, Calum
collection PubMed
description We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables.
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spelling pubmed-58699012018-03-28 Magnetic zero-modes, vortices and Cartan geometry Ross, Calum Schroers, Bernd J. Lett Math Phys Article We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables. Springer Netherlands 2017-11-07 2018 /pmc/articles/PMC5869901/ /pubmed/29606790 http://dx.doi.org/10.1007/s11005-017-1023-2 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Ross, Calum
Schroers, Bernd J.
Magnetic zero-modes, vortices and Cartan geometry
title Magnetic zero-modes, vortices and Cartan geometry
title_full Magnetic zero-modes, vortices and Cartan geometry
title_fullStr Magnetic zero-modes, vortices and Cartan geometry
title_full_unstemmed Magnetic zero-modes, vortices and Cartan geometry
title_short Magnetic zero-modes, vortices and Cartan geometry
title_sort magnetic zero-modes, vortices and cartan geometry
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5869901/
https://www.ncbi.nlm.nih.gov/pubmed/29606790
http://dx.doi.org/10.1007/s11005-017-1023-2
work_keys_str_mv AT rosscalum magneticzeromodesvorticesandcartangeometry
AT schroersberndj magneticzeromodesvorticesandcartangeometry

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