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.

中文翻译：

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时空叶、四元数和打结的光

研究真空中麦克斯韦方程的打结解的几种补充方法现已在文献中提供。然而，只取得了对它们进行统一描述的部分结果。为了对辩论有所了解，我们考察了看待现有形式主义之间关系的新方法。特别是，结合四元数和时空叶的机制，我们展示了在电磁 Hopfion 的情况下，贝特曼对和 Rañada 复数图是如何联系在一起的。类似的方法是否适用于更复杂的解决方案仍然是一个悬而未决的问题。