Related papers: Skyrmions, Rational Maps & Scaling Identities
We discuss an ansatz for Skyrme fields in three dimensions which uses rational maps between Riemann spheres, and produces shell-like structures of polyhedral form. Houghton, Manton and Sutcliffe showed that a single rational map gives good…
We apply two very different approaches to calculate Skyrmions with baryon number B less than 23. The first employs the rational map ansatz, where approximate charge B Skyrmions are constructed from a degree B rational map between Riemann…
The Skyrme crystal is built up of repeating units similar to the cubic Skyrmion of baryon number 4. Using this as guide, we construct new Skyrmion solutions in the massive pion case, with various baryon numbers up to 108. Most of our…
This paper discusses multi-skyrmions on the 3-sphere with variable radius L using the rational map ansatz. For baryon number B = 3,...,9 this ansatz produces the lowest energy solutions known so far. By considering the geometry of the model…
A new method is introduced to construct approximations to Skyrmions that are explicit rational functions of the spatial Cartesian coordinates. The scheme uses ADHM data of a Yang-Mills instanton to produce a Skyrmion with a baryon number…
We discuss the similarities between BPS monopoles and Skyrmions, and point to an underlying connection in terms of rational maps between Riemann spheres. This involves the introduction of a new ansatz for Skyrme fields. We use this to…
Following Marleau, we study an extended version of the Skyrme model to which a sixth order term has been added to the Lagrangian and we analyse some of its classical properties. We compute the multi-Skyrmion solutions numerically for up to…
We find exact solutions for Skyrmions for the Skyrme-like models. Constructing first the recursion formulae at small and large distance behavior, we proceed by implementing these constraints to a chosen parametrization of the solutions. The…
We introduce a simple mathematical expression based on rational maps to construct ideal paraxial optical skyrmions fields including Neel-type and Bloch-type skyrmions, anti-skyrmions, bimerons and multi-skyrmions, including skyrmion…
The Skyrmion number of paraxial optical Skyrmions can be defined solely via their polarization singularities and associated winding numbers, using a mathematical derivation that exploits Stokes's theorem. It is demonstrated that this…
We study the vibration modes of the Skyrme model within the rational map ansatz. We show that the vibrations of the radial profiles and the rational maps are decoupled and we consider explicitly the case B=1, B=2 and B=4. We then compare…
The rational map ansatz of Houghton et al \cite{HMS} is generalised by allowing the profile function, usually a function of $r$, to depend also on $z$ and $\bar{z}$. It is shown that, within this ansatz, the energies of the lowest $B=2,3,4$…
Recently we have presented in hep-th/9811071 an ansatz which allows us to construct skyrmion fields from the harmonic maps of $S\sp2$ to $CP\sp{N-1}$. In this paper we examine this construction in detail and use it to construct, in an…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
The spherically symmetric hedgehog ansatz used in the description of the skyrmion is believed to be inadequate for the rotational states such as the nucleon (I=J=1/2) and the Delta (I=J=3/2) due to centrifugal forces. We study here a simple…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
We construct globally regular gravitating Skyrmions, which possess only discrete symmetries. In particular, we present tetrahedral and cubic Skyrmions. The SU(2) Skyrme field is parametrized by an improved harmonic map ansatz. Consistency…
In present paper we show that many properties of the baby skyrmions, which have been determined numerically, can be understood in terms of an analytic approximation. In particular, we show that this approximation captures properties of the…
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…