A point particle model of lightly bound skyrmions

TL;DR

This paper introduces a point particle model for lightly bound skyrmions that accurately reproduces static solutions and allows for quantization, providing insights into their structure and quantum states.

Contribution

The paper develops a novel point particle model for skyrmions that simplifies analysis while matching known static solutions and enabling quantization of their quantum states.

Findings

Model reproduces static energy minimizers for B=1 to 8.

Identifies large sets of solutions for B=9 to 23 resembling face-centered cubic lattice subsets.

Provides an algorithm for symmetry group computation and Finkelstein-Rubinstein constraints.

Abstract

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number $1\leq B\leq 8$ obtained by numerical simulation of the full field theory. For $9\leq B\leq 23$, a large number of static solutions of the point particle model are found, all closely resembling size $B$ subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.