Electromagnetic knots from de Sitter space

TL;DR

This paper constructs explicit electromagnetic knot solutions on de Sitter space using conformal mappings from Minkowski space, and finds all SU(2) Yang-Mills solutions through reduction to Newton's equations.

Contribution

It provides a complete basis of rational electromagnetic knot solutions on de Sitter space and introduces a method to derive SU(2) Yang-Mills solutions via reduction to classical mechanics.

Findings

Explicit electromagnetic knot solutions on de Sitter space

Complete basis of rational electromagnetic knots

New SU(2) Yang-Mills solutions from Newton's equations

Abstract

We find all analytic SU(2) Yang-Mills solutions on de Sitter space by reducing the field equations to Newton's equation for a particle in a particular 3d potential and solving the latter in a special case. In contrast, Maxwell's equations on de Sitter space can be solved in generality, by separating them in hysperspherical coordinates. Employing a well-known conformal map between (half of) de Sitter space and (the future half of) Minkowski space, the Maxwell solutions are mapped to a complete basis of rational electromagnetic knot configurations. We discuss some of their properties and illustrate the construction method with two nontrivial examples given by rational functions of increasing complexity. The material is partly based on [1,2].