Electromagnetic Knots Research Articles

Two properties of electromagnetic knots

We prove two properties of the electromagnetic knots in empty space. First, that any standard radiation fields (i.e. satisfying E · B = 0 ) coincide locally with an electromagnetic knot. Second, that the electric and magnetic helicities of any knot are equal. These results can be used as a basis for a topological model of electromagnetism.

Electromagnetic knots

We consider electromagnetic knots, defined as standard classical electromagnetic waves in empty space, characterized by two integers n m and n e, such that all the force lines are closed and any pair of magnetic (electric) lines are linked with linking number n m ( n e). Some of their properties are studied.

Knotted solutions of the Maxwell equations in vacuum

It is shown that there exist electromagnetic knots, which are standard electromagnetic fields in which any pair of magnetic lines whatsoever (or of electric lines) are linked and the magnetic helicity has the value integral A.Bd 3r-na, n being a topological constant of the motion given by a Hopf index and a a certain action constant. A family of n=1 knots is obtained, the projection of spin on three-momentum being equal to a.