Knotted solutions of the Maxwell equations in vaccum

Abstract

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 ƒ A * B d^(3)r = na, "n" being a topological constant of the motion given by a Hopf index and B a certain action constant. A family of n = 1 knots is obtained, the projection of spin on three-momentum being equal to a.