Slow equivariant lump dynamics on the two sphere

TL;DR

This paper investigates the low-energy rotationally equivariant dynamics of CP^1 lumps on the two-sphere, analyzing the moduli space's geometry and near-singular behaviors through geodesic flow approximations.

Contribution

It provides a detailed geometric analysis of the moduli space for CP^1 lumps on S^2, including volume, curvature, and near-singular dynamics insights.

Findings

Computed volume and curvature of the moduli space.

Analyzed geodesic flow on the completed moduli space.

Gained understanding of nearly singular lump dynamics.

Abstract

The low-energy, rotationally equivariant dynamics of n CP^1 lumps on S^2 is studied within the approximation of geodesic motion in the moduli space of static solutions. The volume and curvature properties of this moduli space are computed. By lifting the geodesic flow to the completion of an n-fold cover of the moduli space, a good understanding of nearly singular lump dynamics within this approximation is obtained.