Singularities of Magnetic Monopoles for Dirac and 't Hooft-Polyakov Theories by Pre-potential Method

TL;DR

This paper investigates the existence of magnetic monopoles in Dirac and 't Hooft-Polyakov theories using a pre-potential approach, confirming singularities in both models through regularization.

Contribution

It introduces a pre-potential method to analyze monopole singularities, providing new insights into their existence in gauge theories.

Findings

Magnetic singularities exist in both Dirac and 't Hooft-Polyakov monopoles.

The pre-potential approach effectively identifies monopole singularities.

Regularization confirms the presence of singularities in both theories.

Abstract

The magnetic monopole is one of the important problems in the early stage of universe as well as observations and experiments on Earth. We study the existence or non-existence of the Dirac and the 't Hooft-Polyakov magnetic monopole theories using the pre-potential $\boldsymbol{C}$, which is defined to derive the vector potential by the curl operation as $\boldsymbol{A}=\nabla \times \boldsymbol{C}$ . We assert that the magnetic singularity exists for the 't Hooft-Polyakov monopole in SO(3) gauge theory, as well as for the Dirac monopole in U(1) gauge theory. The regularization method confirms our assertion.