The interaction energy of well - separated Skyrme solitons
نویسندگان
چکیده
We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space. We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons' multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.
منابع مشابه
On the existence of minima in the Skyrme model
Well-separated Skyrme solitons of arbitrary degree attract after a suitable relative rotation in space and iso-space, provided the orders of the solitons’ leading multipoles do not differ by more than two. I summarise the derivation of this result, obtained jointly with Manton and Singer, and discuss to what extent its combination with earlier results of Esteban allows one to deduce the existen...
متن کاملMultisolitons in a Two-dimensional Skyrme Model
The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Skyrme model where physical space is twodimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solito...
متن کاملHopf Solitons on the Lattice
Hopf solitons in the Skyrme-Faddeev model — S 2-valued fields on R 3 with Skyrme dynamics — are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S 2-valued fields on the cubic lattice Z 3 with a nearest-neighbour interaction. For suitable choices of the interaction, topological solitons exist on the lattice. Their appearance is remarkably simil...
متن کاملMulti-soliton Dynamics in the Skyrme Model
We exhibit the dynamical scattering of multi-solitons in the Skyrme model for configurations with charge two, three and four. First, we construct maximally attractive configurations from a simple profile function and the product ansatz. Then using a sophisticated numerical algorithm, initially well-separated skyrmions in approximately symmetric configurations are shown to scatter through the kn...
متن کامل/ 01 09 03 4 v 2 2 1 Ja n 20 02 The 1 - soliton in the SO ( 3 ) gauged Skyrme model with mass term
The solitons of the SO(3) gauged Skyrme model with no pion-mass potential were studied in Refs. [1, 2]. Here, the effects of the inclusion of this potential are studied. In contrast with the (ungauged) Skyrme model, where the effect of this potential on the solitons is marginal, here it turns out to be decisive, resulting in very different dependence of the energy as a function of the Skyrme co...
متن کامل