Spacetime foliations, quaternions and knotted light

Abstract

Several complementary approaches to investigate knotted solutions of Maxwell’s equations in vacuum are now available in literature. However, only partial results towards a unified description of them have been achieved. In order to shed some light on the debate, we inspect new ways to view relations between existing formalisms. In particular, combining the machinery of quaternions and spacetime foliations, we show how the Bateman pairs and Rañada complex maps are tied together in the case of the electromagnetic Hopfion. It is still an open question whether a similar approach applies to more complex solutions.