A note on Chern-Simons CP(1) solitons

TL;DR

This paper investigates the properties of solitons in a gauged CP(1) Chern-Simons system, revealing a relation between electric field divergence and topological charges, and establishing the topological charge as an energy bound.

Contribution

It introduces a new relation between electric field divergence and topological charge densities in gauged CP(1) Chern-Simons systems, and demonstrates the topological charge bounds the energy.

Findings

Electric field divergence relates to topological charge densities.

Topological charge acts as a lower bound for energy.

Analysis uses an ansatz to elucidate field relations.

Abstract

We study a gauged CP(1) Chern-Simons system. Using the equations of motion we find, for a static field configuration, that the divergence of the electric field is related to the electric and the CP(1) topological charge densities . We discuss this relation in terms of an ansatz for the fields and use it to show that the CP(1) topological charge is a bound of the energy.