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Null electromagnetic fields from dilatation and rotation transformations of the hopfion

AuthorsArrayás, Manuel; Rañada, Antonio F.; Tiemblo, Alfredo ; Trueba, José L.
Bateman construction
Null fields
Issue Date2-Sep-2019
PublisherMolecular Diversity Preservation International
CitationSymmetry 11: 9 (2019)
AbstractThe 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.
Description17 pags., 4 figs. -- Open Access funded by Creative Commons Atribution Licence 4.0
Publisher version (URL)http://dx.doi.org/10.3390/sym11091105
Identifiersdoi: 10.3390/sym11091105
issn: 2073-8994
Appears in Collections:(CFMAC-IFF) Artículos
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