The Energy of Scattering Solitons in the Ward Model

The energy density of a scattering soliton solution in Ward's integrable chiral model is shown to be instantaneously the same as the energy density of a static multi-lump solution of the \CP^3 sigma model. This explains the quantization of the total energy in the Ward model.Comment: 12 pages, 2 figure

Electroweak Strings, Zero Modes and Baryon Number

The Dirac equations for leptons and quarks in the background of an electroweak $Z-$string have zero mode solutions. If two loops of electroweak string are linked, the zero modes on one of the loops interacts with the other loop via an Aharanov-Bohm interaction. The effects of this interaction are briefly discussed and it is shown that the fermions induce a baryon number on linked loops of $Z-$string. (Submitted to Proceedings of "Trends in Astrophysics" Conference, Stockholm, 1994.)Comment: LaTeX using espcrc2.sty (version 2.5) (hit return on error messages), 3 page

Skyrmions, Rational Maps & Scaling Identities

Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the true Skyrmions are more oblate or prolate.Comment: 13 pages, 3 figure

Angularly localized Skyrmions

Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and angularly localized wavefunctions for them are found. By combining a few low angular momentum states, one can construct a quantum state whose spatial density is close to that of the classical Skyrmion, and has the same symmetries. For the B=1 case we find the best localized wavefunction among linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced localization compared to the classical solution. For B=4, where the classical Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by combining the $j=0$ ground state with the lowest rotationally excited $j=4$ state. We use the rational map approximation to compare the classical and quantum baryon densities in the B=2 and B=4 cases.Comment: 22 page

On the electromagnetic form factors of the proton from generalized Skyrme models

We compare the prediction of Skyrme-like effective Lagrangians with data for electromagnetic form factors of proton and consider the possibility of fixing the parameters of these higher-order Lagrangians. Our results indicate that one or two-parameter models can lead to better agreement with the data but more accurate determination of the effective Lagragian faces theoretical uncertainties.Comment: 8 pages, 2 figures, revte

Reparametrising the Skyrme Model using the Lithium-6 Nucleus

The minimal energy B=6 solution of the Skyrme model is a static soliton with $D_{4d}$ symmetry. The symmetries of the solution imply that the quantum numbers of the ground state are the same as those of the Lithium-6 nucleus. This identification is considered further by obtaining expressions for the mean charge radius and quadrupole moment, dependent only on the Skyrme model parameters $e$ (a dimensionless constant) and $F_\pi$ (the pion decay constant). The optimal values of these parameters have often been deliberated upon, and we propose, for $B>2$, changing them from those which are most commonly accepted. We obtain specific values for these parameters for B=6, by matching with properties of the Lithium-6 nucleus. We find further support for the new values by reconsidering the $\alpha$-particle and deuteron as quantized B=4 and B=2 Skyrmions.Comment: 18 page

Solitons in a Baby-Skyrme model with invariance under area preserving diffeomorphisms

We study the properties of soliton solutions in an analog of the Skyrme model in 2+1 dimensions whose Lagrangian contains the Skyrme term and the mass term, but no usual kinetic term. The model admits a symmetry under area preserving diffeomorphisms. We solve the dynamical equations of motion analytically for the case of spinning isolated baryon type solitons. We take fully into account the induced deformation of the spinning Skyrmions and the consequent modification of its moment of inertia to give an analytical example of related numerical behaviour found by Piette et al.. We solve the equations of motion also for the case of an infinite, open string, and a closed annular string. In each case, the solitons are of finite extent, so called "compactons", being exactly the vacuum outside a compact region. We end with indications on the scattering of baby-Skyrmions, as well as some considerations as the properties of solitons on a curved space.Comment: 30 pages, 5 figures, revtex, major modifications, conclusions modifie

Resonance structures in coupled two-component ϕ4\phi^4 model

We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and kink-non-topological soliton (lump) bound state. Collision of these solitons leads to very reach resonance structure which is related to reversible energy exchange between the kinks, non-topological solitons and the internal vibrational modes. Various channels of the collisions are discussed, it is shown there is a new type of self-similar fractal structure which appears in the collisions of the relativistic kinks, there the width of the resonance windows increases with the increase of the impact velocity. An analytical approximation scheme is discussed in the limit of the perturbative coupling between the sectors. Considering the spectrum of linear fluctuations around the solitons we found that the double kink configuration is unstable if the coupling constant between the sectors is negative.Comment: 21 pages, 19 figure