Hopfions interaction from the viewpoint of the product ansatz

Abstract

We discuss the relation between the solutions of the Skyrme model of lower degrees and the corresponding axially symmetric Hopfions which is given by the projection onto the coset space SU(2)/U(1). The interaction energy of the Hopfions is evaluated directly from the product ansatz. Our results show that if the separation between the constituents is not very small, the product ansatz can be considered as a relatively good approximation to the general pattern of the charge one Hopfions interaction both in repulsive and attractive channel.