Topological structure of the vortex solution in Jackiw-Pi model

TL;DR

This paper analyzes the topological structure of vortex solutions in the Jackiw-Pi model, revealing their relation to topological invariants and flux quantization, and examining their angular momentum properties.

Contribution

It introduces a topological analysis of Jackiw-Pi vortices using gauge potential decomposition and links vortex solutions to topological numbers like Hopf index and Brouwer degree.

Findings

Established the relationship between Chern-Simons vortices and topological numbers.

Derived flux quantization conditions for vortex solutions.

Expressed vortex angular momentum in terms of flux.

Abstract

By using $\phi$ -mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortices solution and topological number which is determined by Hopf index and and Brouwer degree. We also give the quantization of flux in the case. Then, we study the angular momentum of the vortex, it can be expressed in terms of the flux.