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Title: Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

Abstract

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow tomore » develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].« less

Authors:
Publication Date:
OSTI Identifier:
22560333
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 371; Journal Issue: Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DUALITY; DYONS; ELECTRODYNAMICS; FLUIDS; GAUGE INVARIANCE; HYDRODYNAMICS; INSTANTONS; MASS; MATHEMATICAL SOLUTIONS; MONOPOLES; YANG-MILLS THEORY

Citation Formats

Kholodenko, Arkady L., E-mail: string@clemson.edu. Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.04.003.
Kholodenko, Arkady L., E-mail: string@clemson.edu. Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots. United States. doi:10.1016/J.AOP.2016.04.003.
Kholodenko, Arkady L., E-mail: string@clemson.edu. 2016. "Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots". United States. doi:10.1016/J.AOP.2016.04.003.
@article{osti_22560333,
title = {Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots},
author = {Kholodenko, Arkady L., E-mail: string@clemson.edu},
abstractNote = {Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].},
doi = {10.1016/J.AOP.2016.04.003},
journal = {Annals of Physics},
number = Complete,
volume = 371,
place = {United States},
year = 2016,
month = 8
}
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