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arXiv · 1711.11144

A new construction of rational electromagnetic knots

Olaf Lechtenfeld·Gleb Zhilin
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Abstract

We set up a correspondence between solutions of the Yang-Mills equations on ${\mathbb R}\times S^3$ and in Minkowski spacetime via de Sitter space. Some known Abelian and non-Abelian exact solutions are rederived. For the Maxwell case we present a straightforward algorithm to generate an infinite number of explicit solutions, with fields and potentials in Minkowski coordinates given by rational functions of increasing complexity. We illustrate our method with a nontrivial example.

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Olaf Lechtenfeld, Gleb Zhilin. 2018-06-08. A new construction of rational electromagnetic knots. https://doi.org/10.1016/j.physleta.2018.04.027

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