Skyrmions and Faddeev-Hopf solitons

  title={Skyrmions and Faddeev-Hopf solitons},
  author={Richard Samuel Ward},
  journal={Physical Review D},
  • R. S. Ward
  • Published 28 July 2004
  • Physics
  • Physical Review D
This paper describes a natural one-parameter family of generalized Skyrme systems, which includes the usual SU(2) Skyrme model and the Skyrme-Faddeev system. Ordinary Skyrmions resemble polyhedral shells, whereas the Hopf-type solutions of the Skyrme-Faddeev model look like closed loops, possibly linked or knotted. By looking at the minimal-energy solutions in various topological classes, and for various values of the parameter, we see how the polyhedral Skyrmions deform into looplike Hopf… 

Figures from this paper

Revisiting the Faddeev-Skyrme model and Hopf solitons

We observe that the Faddeev-Skyrme model emerges as a low-energy limit of scalar QED with two charged scalar fields and a selfinteraction potential of a special form (inspired by supersymmetric QCD).

Generalized Skyrme crystals.

Toroidal solitons in Nicole-type models

Abstract.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

Skyrmions and hopfions in three-dimensional frustrated magnets

A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic Skyrmions. In the continuum approximation this model reduces to a

Lattices of generalized Skyrmions

Generalized Skyrme systems are those which include both the Skyrme and the Skyrme-Faddeev models through an interpolating parameter \alpha \in [0,1] the former corresponds to \alpha=0 and the latter

Skyrmions and Hopfions in 3D Frustrated Magnets

A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic Skyrmions. In the continuum approximation this model reduces to a

Linking number of vortices as baryon number

We show that the topological degree of a Skyrmion field is the same as the Hopf charge of the field under the Hopf map and thus equals the linking number of the preimages of two points on the

Classically spinning and isospinning non-linear σ-model solitons

We investigate classically (iso)spinning topological soliton solutions in (2+1)- and (3+1)-dimensional models; more explicitly isospinning lump solutions in (2+1) dimensions, Skyrme solitons in (2+1)

Knots and links in the order parameter distributions of strongly correlated systems

Research on the coherent distribution of order parameters determining phase existence regions in the two-component Ginzburg–Landau model is reviewed. A major result of this research, obtained by

Field Theories and Vortices with Nontrivial Geometry

This thesis investigates aspects of field theories and soliton solutions with nontrivial topology. In particular we explore the following effective models: a limited sector of the scalar Electrowea



Hopf solitons on S3 and 3

The Skyrme-Faddeev system, a modified O(3) sigma model in three space dimensions, admits topological solitons with nonzero Hopf number. One may learn something about these solitons by considering the

Solitons, links and knots

  • R. BattyeP. Sutcliffe
  • Physics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1999
Using numerical simulations of the full nonlinear equations of motion, we investigate topological solitons of the Skyrme–Faddeev system, which is a modified O(3) sigma model in three space

The interaction of two Hopf solitons

Geometry of Skyrmions

A Skyrmion may be regarded as a topologically non-trivial map from one Riemannian manifold to another, minimizing a particular energy functional. We discuss the geometrical interpretation of this

Faddeev-Hopf knots: dynamics of linked un-knots

Classical gauge vacua as knots

Skyrmions, fullerenes and rational maps

We apply two very different approaches to calculate Skyrmions with baryon number B ≤ 22. The first employs the rational map ansatz, where approximate charge B Skyrmions are constructed from a degree

Static solitons with nonzero Hopf number

We investigate a generalized nonlinear O(3) {sigma} model in three space dimensions where the fields are maps from R{sup 3}{union}{l_brace}{infinity}{r_brace} to S{sup 2}. Such maps are classified by

Knots and Particles

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly

Hidden symmetry and knot solitons in a charged two-condensate Bose system

We show that a charged two-condensate Ginzburg-Landau model or equivalently a Gross-Pitaevskii functional for two charged Bose condensates, can be mapped onto a version of the nonlinear O(3) sigma ...