On the Fibration Defined by the Field Lines of a Knotted Class of Electromagnetic Fields at a Particular Time

Abstract

A class of vacuum electromagnetic fields in which the field lines are knotted curves are reviewed. The class is obtained from two complex functions at a particular instant t = 0 so they inherit the topological properties of red the level curves of these functions. We study the complete topological structure defined by the magnetic and electric field lines at t = 0 . This structure is not conserved in time in general, although it is possible to red find special cases in which the field lines are topologically equivalent for every value of t.

Keywords

• electromagnetic knots
• torus knots
• maxwell equations in vacuum