Electromagnetic knots from de Sitter space

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].