Knots and the Maxwell Equations

TL;DR

This paper reviews topologically non-trivial solutions to Maxwell's equations, explores their relation to knot theory, and generalizes these solutions to nonlinear electrodynamics, highlighting their mathematical and physical significance.

Contribution

It provides a comprehensive review of Ra ilde{n}ada solutions and introduces a novel generalization to nonlinear electrodynamics, expanding the understanding of electromagnetic knots.

Findings

Ra ilde{n}ada solutions describe knotted electromagnetic fields

Established connection between electromagnetic fields and knot theory

Generalized solutions to nonlinear electrodynamics

Abstract

In this chapter, we review the Ra\~{n}ada field line solutions of Maxwell's equations in the vacuum, which describe a topologically non-trivial electromagnetic field, as well as their relation with the knot theory. Also, we present a generalization of these solutions to the non-linear electrodynamics recently published in the literature.