Can magnetic monopoles and massive photons coexist in the framework of the same classical theory?

TL;DR

This paper demonstrates that in classical electromagnetism, magnetic monopoles and massive photons cannot coexist consistently, as the theory inherently predicts a visible string attached to monopoles.

Contribution

It shows that the inconsistency between magnetic monopoles and massive photons exists at the classical level without quantum or limiting approximations.

Findings

The classical theory predicts a visible string attached to monopoles with massive photons.

The inconsistency is intrinsic to the classical framework, not just quantum effects.

Massive photons do not resolve the classical incompatibility with magnetic monopoles.

Abstract

It is well known that one cannot construct a self-consistent quantum field theory describing the non-relativistic electromagnetic interaction mediated by massive photons between a point-like electric charge and a magnetic monopole. We show that, indeed, this inconsistency arises in the classical theory itself. No semi-classic approximation or limiting procedure for the Dirac constant approaching to zero is used. As a result, the string attached to the monopole emerges as visible also if finite-range electromagnetic interactions are considered in classical framework.