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Volume 347 - Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2018) - Session: Dualities and Generalized Geometries
A new construction of rational electromagnetic knots
O. Lechtenfeld,* G. Zhilin
*corresponding author
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Published on: 2019 September 19
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 some nontrivial examples.
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