# Some characterizations of Dirac type singularity of monopoles

## TL;DR

This paper investigates the nature of Dirac type singularities in monopoles within 3D Euclidean space, providing two new characterizations based on growth rates of specific mathematical quantities.

## Contribution

It introduces two novel characterizations of Dirac type singularities in monopoles, enhancing understanding of their mathematical structure.

## Key findings

- Characterization via growth order of invariant sections
- Characterization via growth order of Higgs fields
- Provides criteria for identifying Dirac type singularities

## Abstract

We study singular monopoles on open subsets in the $3$-dimensional Euclidean space. We give two characterizations of Dirac type singularities. One is given in terms of the growth order of the norms of sections which are invariant by the scattering map. The other is given in terms of the growth order of the norms of the Higgs fields.