Related papers: Folding in the Skyrme Model
For any 3-manifold M and any nonnegative integer g, we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus g and without Morse index bounds. On any spherical space form S^3/Gamma we…
The Skyrme model is a classical field theory which has topological soliton solutions. These solitons are candidates for describing nuclei, with an identification between the numbers of solitons and nucleons. We have computed numerically,…
A set of classical solutions of a singular type is found in a 5D SUSY bulk-boundary system. The "parallel" configuration, where the whole components of fields or branes are parallel in the iso-space, naturally appears. It has three {\it…
We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or…
We study static solutions of the standard Skyrme model with a pion mass. Using approximately $10^5$ pseudo-random initial configurations made of single Skyrmions in the non-symmetrized product Ansatz and an automatic detection of repeated…
The new ansatz which is the SO(3) group soliton was defined for the SU(3) Skyrme model. The model is considered in noncanonical bases $SU(3)\supset SO(3)$ for the state vectors. A complete canonical quantization of the model have been…
A Skyrme type energy functional for maps $\varphi$ from an oriented Riemannian 3-manifold $M$ to a contact 3-manifold $N$ is defined, generalizing the BPS Skyrme energy of Ferreira and Zakrzewski. This energy has a topological lower bound,…
The quantum Skyrme model is considered in non canonical bases SU(3) > SO(3) for the state vectors. A rational map ansatz is used to describe the soliton with the topological number bigger than one. The canonical quantization of the…
Static polarizabilities of the low--lying $1/2^+$ baryons are studied within the collective coordinate approach to the three flavor generalization of the Skyrme model; in particular, magnetic polarizabilities are considered. Predicted…
We analyze the mechanism of condensation of orientational moduli (as introduced in [25]) on multi-Skyrmionic configurations of the four-dimensional Skyrme model. The present analysis reveals interesting novel features. First of all, the…
Special generic maps are smooth maps at each singular point of which we can represent as $(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$ for suitable coordinates. Morse functions with exactly two singular points on…
Fold maps are higher dimensional versions of Morse functions, which play important roles in the studies of smooth manifolds, and such general maps also have been fundamental tools in the studies of smooth manifolds by using generic maps. In…
We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…
I consider configuration spaces for $N$-body problems, gauge theories and for GR in both geometrodynamical and Ashtekar variables forms, including minisuperspace and inhomogeneous perturbations thereabout in the former case. These examples…
Localized static solutions of the 2D-O(3) model are investigated in a representation with the 3-vector field $\vec Phi$ split into the unit vector $\hat Phi$ and the modulus $\Phi$. As in the nonlinear version of the model this allows for…
Within the class of field theories with the field contents of the Skyrme model, one submodel can be found which consists of the square of the baryon current and a potential term only. For this submodel, a Bogomolny bound exists and the…
We show that every small resolution of a three-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional…
By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five-dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of…
A set of classical solutions of a singular type is found in a 5D SUSY bulk-boundary system. The "parallel" configuration, where the whole components of fields or branes are parallel in the iso-space, naturally appears. It has three {\it…
Numerical methods are used to compute sphaleron solutions of the Skyrme model. These solutions have topological charge zero and are axially symmetric, consisting of an axial charge n Skyrmion and an axial charge -n antiSkyrmion (with n…