One-dimensional topologically nontrivial solutions in the Skyrme model

Abstract

We consider the Skyrme model using the explicit parameterization of the rotation group SO(3) through elements of its algebra. Topologically nontrivial solutions already arise even in the one-dimensional case because the fundamental group of SO(3) is Z_2. We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy among them. We propose a new class of projective models whose target spaces are arbitrary real projective spaces RP^d.