Field of the Magnetic Monopole

TL;DR

This paper demonstrates that the magnetic monopole field cannot be represented by a vector potential, challenging the mathematical foundation of the original quantization prediction of magnetic charge.

Contribution

It reveals a fundamental mathematical inconsistency in representing magnetic monopoles with vector potentials based on Helmholtz decomposition.

Findings

Vector potential cannot represent stationary magnetic monopole fields.

Using vector potential in monopole theory violates mathematical principles.

Implications for the theoretical prediction of magnetic charge quantization.

Abstract

This paper shows that based upon the Helmholtz decomposition theorem the field of a stationary magnetic monopole, assuming it exists, cannot be represented by a vector potential. Persisting to use vector potential in monopole representation violates fundamentals of mathematics. The importance of this finding is that the vector potential representation was crucial to the original prediction of the quantized value for a magnetic charge.