Cross-fertilization of Ferreira's Hopfions And Electromagnetic Knots

The interrelation between Ferreira’s Hopf solitons of a conformal nonlinear $\sigma$ model and the electromagnetic knots found by Ra$\tilde{\mathrm{n}}$ada et al. is investigated. It is shown that the electromagnetic knots yield exact solutions of the conformal nonlinear $\sigma$ model different from those obtained by Ferreira. Conversely, It is discussed that Ferreira’s solutions realize magnetic knots. The energy associated with these two kinds of knots are compared. The structure of the electric charge distribution and the electric current density associated with the magnetic knots is investigated.