Magnetic Monopoles with No Strings Attached: A Portal to the Dark Side of Dual Electrodynamics

TL;DR

This paper develops a dual-symmetric formulation of electromagnetism with magnetic monopoles that avoids Dirac strings and introduces a new coupling constant, potentially linking electric and magnetic sectors otherwise considered separate.

Contribution

It presents a local Lagrangian for SO(2) dual electromagnetism with magnetic monopoles, avoiding Dirac strings and proposing a new coupling constant that connects electric and magnetic charges.

Findings

A local Lagrangian for dual electromagnetism is formulated.

A generalized Lorentz force involving a new coupling constant is derived.

The new coupling constant could enable interactions between electric and magnetic sectors.

Abstract

It has long been known that in the absence of electric charges and currents, Maxwell's electromagnetism in 4 dimensional vacuum Minkowski space-time is invariant under SO(2) dual transformations that mix its electric and magnetic fields. Extending this symmetry to include the coupling to electrically charged matter, requires a dual coupling to magnetically charged matter as well, leading to Maxwell equations for SO(2) dual electrodynamics. Based on a doubled ensemble of SO(2) dual 4-vector gauge potentials which does away with the need of Dirac string singularities for magnetic monopoles, a local Lagrangian action principle for SO(2) dual electromagnetism is known, which manifestly displays all the required space-time and internal symmetries, and reduces to the experimentally well established Maxwell electrodynamics in the absence of magnetic charges and currents. Applying the same considerations for the matter action of electrically and magnetically charged point particles, a unique SO(2) dual generalised Lorentz force is identified for SO(2) dual electrodynamics, truly different from the usual SO(2) dual invariant choice motivated by simplicity, but yet made arbitrarily and which does not derive from some action principle. This generalised Lorentz force involves a single real and new coupling constant of unknown value, without the requirement of a Dirac-Schwinger-Zwanziger quantisation condition for electric and magnetic charges of dyons. A physical consequence for SO(2) dual electrodynamics of this coupling constant if nonvanishing, is to open a channel, or portal between the otherwise mutually totally ``dark'' sectors of electric and magnetic charges for electromagnetic interactions.