Null electromagnetic fields from dilatation and rotation transformations of the hopfion
| Autor: | José L. Trueba, Antonio F. Rañada, Manuel Arrayás, Alfredo Tiemblo |
|---|---|
| Přispěvatelé: | Ministerio de Ciencia, Innovación y Universidades (España), SCOAP |
| Rok vydání: | 2019 |
| Předmět: |
Electromagnetic field
Physics Physics and Astronomy (miscellaneous) Field line General Mathematics lcsh:Mathematics Bateman construction Null fields lcsh:QA1-939 01 natural sciences 010305 fluids & plasmas Homothetic transformation symbols.namesake Knot (unit) Classical mechanics Maxwell's equations Chemistry (miscellaneous) Hopfion 0103 physical sciences Computer Science (miscellaneous) symbols 010306 general physics |
| Zdroj: | Symmetry, Vol 11, Iss 9, p 1105 (2019) Symmetry Volume 11 Issue 9 Digital.CSIC. Repositorio Institucional del CSIC instname |
| Popis: | 17 pags., 4 figs. -- Open Access funded by Creative Commons Atribution Licence 4.0 The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion. This research was funded by the Spanish Ministry of Economy and Competitiveness grant number ESP2017-86263-C4-3-R. |
| Databáze: | OpenAIRE |
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