The Bifurcation of the Topological Structure in the Sunspot's Electric Topological Current with Locally Gauge-invariant Maxwell-Chern-Simons Term

TL;DR

This paper investigates the topological structure and bifurcation behavior of electric currents in a gauge-invariant Maxwell-Chern-Simons model, revealing quantized charges and local topological changes during evolution.

Contribution

It introduces a detailed analysis of the bifurcation phenomena in electric topological currents within a Maxwell-Chern-Simons framework, emphasizing topological charge quantization and local structure dynamics.

Findings

Electric topological charge is quantized by winding number.

Electric current generation and annihilation occur at limit points.

Splitting and merging of currents happen at bifurcation points.

Abstract

The topological structure of the electric topological current of the locally gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The electric topological charge is quantized in term of winding number. The Hopf indices and Brouwer degree labeled the local topological structure of the electric topological current. Using $\Phi $-mapping method and implicity theory, the electric topological current is found generating or annihilating at the limit points and splitting or merging at the bifurcate points. The total electric charge holds invariant during the evolution.