Classical electromagnetic field theory in the presence of magnetic sources

TL;DR

This paper reformulates classical electromagnetic theory with magnetic sources using new potential vectors, achieving Lorentz covariance and duality symmetry, and derives Maxwell's equations and dyon dynamics from a consistent Lagrangian.

Contribution

Introduction of two new 4D potential vectors enabling a Lorentz covariant and duality symmetric formulation of Maxwell's theory with magnetic sources.

Findings

Formulation of Maxwell's equations with magnetic sources using new potentials

Derivation of equations of motion for dyons from the action principle

Establishment of a consistent Lagrangian for the extended theory

Abstract

Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.