Steffen Krusch

Spinning skyrmions and the Skyrme parameters

The traditional approach to fixing the parameters of the Skyrme model requires the energy of a spinning skyrmion to reproduce the nucleon and delta masses. The standard Skyrme parameters, which are used almost exclusively, fix the pion mass to its experimental value and fit the two remaining Skyrme parameters by approximating the spinning skyrmion as a rigid body. In this Letter we remove the rigid body approximation and perform numerical calculations which allow the spinning skyrmion to deform and break spherical symmetry. The results show that if the pion mass is set to its experimental value then the nucleon and delta masses cannot be reproduced for any values of the Skyrme parameters; the commonly used Skyrme parameters are simply an artifact of the rigid body approximation. However, if the pion mass is taken to be substantially larger than its experimental value then the nucleon and delta masses can be reproduced. This result has a significant effect on the structure of multi-skyrmions.

Homotopy of Rational Maps and the Quantization of Skyrmions

The Skyrme model is a classical field theory which models the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein constraints into account. The aim of this paper is to show how to calculate these FR constraints directly from the rational map ansatz using basic homotopy theory. We then apply this construction in order to quantize the Skyrme model in the simplest approximation, the zero mode quantization. This is carried out for up to 22 nucleons, and the results are compared to experiment.

Exact moduli space metrics for hyperbolic vortex polygons

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Σn,m, are spaces of Cn-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N−n coincident vortices at the polygon’s center. The geometric properties of Σn,m are investigated, and it is found that Σn,n−1 is isometric to the hyperbolic plane of curvature −(3πn)−1. The geodesic flow on Σn,m and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong [“The dynamics of Chern-Simons vortices,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.

S**3 skyrmions and the rational map ansatz

This paper discusses multi-Skyrmions on the 3-sphere S3 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 we find an approximate analytic formula for the shape function. This provides an insight into why Skyrmions have a shell-like structure.

SPHALERONS IN THE SKYRME MODEL

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 anti-Skyrmion (with n > 1), balanced in unstable equilibrium. The energy is slightly less than twice the energy of the axially symmetric charge n Skyrmion. A similar configuration with n = 1 does not produce a sphaleron solution, and this difference is explained by considering the interaction of asymptotic pion dipole fields. For sphaleron solutions with n > 4, the positions of the Skyrmion and anti-Skyrmion merge to form a circle, rather than isolated points, and there are some features in common with Hopf solitons of the Skyrme-Faddeev model.

Dynamics of Multi-kinks in the Presence of Wells and Barriers

Sine-Gordon kinks are a much studied integrable system that possesses multi-soliton solutions. Recent studies on sine-Gordon kinks with spacedependent square-well-type potentials have revealed interesting dynamics of a single kink interacting with wells and barriers. In this paper, we study a class of smooth space-dependent potentials and discuss the dynamics of one kink in the presence of different wells. We also present values for the critical velocity for different types of barriers. Furthermore, we study two kinks interacting with various wells and describe interesting trajectories such as double-trapping, kink knock-out and double-escape.

Folding in the Skyrme model

There are only three stable singularities of a differentiable map between threedimensional manifolds, namely folds, cusps and swallowtails. A Skyrme configuration is a map from space to SU2, and its singularities correspond to the points where the baryon density vanishes. In this paper we consider the singularity structure of Skyrme configurations. The Skyrme model can only be solved numerically. However, there are good analytic �

Fermionic Quantization of Hopf Solitons

In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q=7.

Finkelstein-Rubinstein constraints for the Skyrme model with pion masses

The Skyrme model is a classical field theory modelling the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein–Rubinstein constraints into account. Recently, a simple formula has been derived to calculate the constraints for Skyrmions which are well approximated by rational maps. However, if a pion mass term is included in the model, Skyrmions of sufficiently large baryon number are no longer well approximated by the rational map ansatz. This paper addresses the question how to calculate Finkelstein–Rubinstein constraints for Skyrme configurations which are only known numerically.

Classically isospinning Skyrmion solutions

We investigate how isospin affects the geometrical shape and energy of classical soliton solutions of topological charges