Topological field patterns of the Yang-Mills theory

TL;DR

This paper introduces a gauge-invariant way to characterize SO(3) Yang-Mills fields using vector fields, linking topological features like monopole charge to Abelian potentials, enhancing understanding of gauge field topology.

Contribution

It presents a novel gauge-invariant characterization of SO(3) gauge fields through vector fields and relates topological charges to Abelian potentials, advancing topological analysis in Yang-Mills theory.

Findings

Gauge fields characterized by gauge-invariant vector fields.

Topological singularities describe monopole charges.

Monopole charge expressed via Abelian vector potential.

Abstract

It is shown that the SO(3) gauge field configurations can be completely characterised by certain gauge invariant vector fields. The singularities of these vector fields describe the topological aspects of the gauge field configurations. The topological (or monopole) charge is expressed in terms of an Abelian vector potential.