One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model

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