The Baby Skyrme Model. Kellen Gillispie and Michael Zlotoff

Abstract

We investigated the properties of solitons using the Baby Skyrme model. This required the use of Monte Carlo methods to simulate solitons in a pion field on S2 (the surface of a sphere). The simulation will yield results on solitons that will extend to the Skyrme model in S3 (the surface of a hyper-sphere). Nuclear physics is largely concerned with two types of particles: mesons and baryons. Baryons have spin ? and are the heavier of the two. Neutrons and protons are examples of baryons. Mesons, the lighter particles, have integer spin. A pion is the lightest meson that feels the nuclear force and is responsible for mediating the nuclear force to the baryons. In the Skyrme model, only meson fields are included in the Lagrangian; baryons emerge as the topological twists (solitons) in the fields. We worked on the Baby Skyrme model, which deals with S2 rather than S3. We quantized the pion field on a lattice. Each point on the lattice was assigned a pion field value where the sum of the squares of the components equals one (the equation of a sphere in S2). Once the simulation was set, Monte Carlo methods were applied to each lattice point. It is important to mention that winding number is the number of times that the range is swept over for one pass of the domain, the position in the lattice. In the Skyrme model, this winding number is a conserved integer.