A new construction of rational electromagnetic knots

TL;DR

This paper introduces a novel method to generate an infinite family of explicit rational electromagnetic field solutions, connecting Yang-Mills equations on different spacetimes, and rederives known solutions.

Contribution

It provides a new construction technique for rational electromagnetic knots and establishes a correspondence between solutions on different spacetime manifolds.

Findings

Infinite set of explicit rational solutions generated

Re-derivation of known Abelian and non-Abelian solutions

Illustration with a nontrivial example

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.