Related papers: Classically Isospinning Hopf Solitons
The strongly coupled limit of the Skyrme-Faddeev-Niemi model (i.e., without quadratic kinetic term) with a potential is considered on the spacetime S^3 x R. For one-vacuum potentials two types of exact Hopf solitons are obtained. Depending…
In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in…
Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for…
The Aratyn-Ferreira-Zimerman (AFZ) model is a conformal field theory in three-dimensional space. It has solutions that are topological solitons classified by an integer-valued Hopf index. There exist infinitely many axial solutions which…
3D topological solitons are marvels of mathematical physics that arise in theoretical models in elementary particle and nuclear physics, condensed matter, and cosmology. A particularly interesting type of them is described by the…
The holonomy of an SU(2) N-instanton in the x^4-direction gives a map from R^3 into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)=S^3 to S^2 gives a configuration for a Hopf…
In this paper we construct explicitly an infinite number of Hopfions (static, soliton solutions with non-zero Hopf topological charges) within the recently proposed 3+1-dimensional, integrable and relativistically invariant field theory.…
We construct static and time-dependent exact soliton solutions with non-trivial Hopf topological charge for a field theory in 3+1 dimensions with the target space being the two dimensional sphere S**2. The model considered is a reduction of…
We construct new solutions of the Faddeev-Skyrme model with a symmetry breaking potential admitting $S^1$ vacuum. It includes, as a limiting case, the usual $SO(3)$ symmetry breaking mass term, another limit corresponds to the potential…
The Faddeev-Skyrme model, a modified O(3) nonlinear sigma model in three space dimensions, is known to admit topological solitons that are stabilized by the Hopf charge. The Faddeev-Skyrme model is also related to the low-energy limits of…
A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological…
Generalized Aratyn-Ferreira-Zimerman O(3) nonlinear sigma model with a particular symmetry breaking term, so-called dielectric function, is discussed. Static multi-soliton configurations with finite energy and nontrivial Hopf index are…
We discuss the $U(1)$ gauged version of the 3+1 dimensional Faddeev-Skyrme model supplemented by the Maxwell term. We show that there exist axially symmetric static solutions coupled to the non-integer toroidal flux of magnetic field, which…
We consider a field theory with target space being the two dimensional sphere S^2 and defined on the space-time S^3 x R. The Lagrangean is the square of the pull-back of the area form on S^2. It is invariant under the conformal group…
The Skyrme-Faddeev model has planar soliton solutions with target space $\mathbb{C}P^N$. An Abelian Chern-Simons term (the Hopf term) in the Lagrangian of the model plays a crucial role for the statistical properties of the solutions.…
The complex eikonal equation in $(3+1)$ dimensions is investigated. It is shown that this equation generates many multi soliton configurations with arbitrary value of the Hopf index. In general, these eikonal hopfions do not have the…
Motivated by the sigma model limit of multicomponent Ginzburg-Landau theory, a version of the Faddeev-Skyrme model is considered in which the scalar field is coupled dynamically to a one-form field called the supercurrent. This coupled…
We find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers $n$ and $m$. It is a (modified) skyrmion in the $z=0$…
We propose a topological soliton or instanton solution with nonzero Hopf invariant to the 3+1D non-Abelian gauge theory coupled with scalar fields. This solution, which we call Hopf soliton, represents a spacetime event that makes a $2\pi$…
The Skyrme-Faddeev model is a (3+1)-dimensional model which has knotted, string-like, soliton solutions. In this paper we investigate a Skyrme-Faddeev model with an SO(3) symmetry breaking potential. We then rescale this model and take the…