# Dirac monopoles and the importance of the usage of appropriate degrees of freedom

## TL;DR

The paper argues that the singularities in Dirac's magnetic monopole theory are due to the choice of fields, not the monopoles themselves, and suggests using singularity-free descriptions for better understanding.

## Contribution

It demonstrates that singularities in Dirac monopoles arise from the field description, not the monopoles, and advocates for alternative, singularity-free geometric descriptions.

## Key findings

- Singularities are due to the field set used, not monopoles.
- Affine connections on spheres exhibit similar singularities.
- Alternative descriptions can eliminate singularities.

## Abstract

We discuss that the singularities appearing in Dirac's formulation of magnetic monopoles are due to the set of fields which he used and not due to the physical properties of magnetic monopoles. We explain in detail that we can find the same algebraic expressions and singularities for the affine connections on the sphere $S^2$, which Dirac found for the U(1) gauge field of magnetic monopoles. Since spheres have no singularities, it is obvious, that these singularities are due to the set of fields which are used to describe the geometry of $S^2$. As there are descriptions of the geometry of spheres without any singularities, we indicate that it would be preferable to use singularity free descriptions of magnetic and also electric monopoles.