The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles

TL;DR

This paper formulates Maxwell's equations with massive photons and magnetic monopoles using spacetime algebra, unifying the theory into a single multi-vector equation and analyzing its symmetries and limiting cases.

Contribution

It introduces a spacetime algebra formulation for massive electrodynamics with monopoles, highlighting symmetries and limiting behaviors in a unified framework.

Findings

Single multi-vector equation describes the theory

Symmetries in massless and massive photon limits

EM-duality invariance as a symmetry of Hamiltonian and Lagrangian densities

Abstract

Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single non-homogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and their symmetries highlighted: massless photons with magnetic monopoles and finite photon mass in the absence of monopoles. Finally, it is shown that the EM-duality invariance is a symmetry of the Hamiltonian density (for Minkowskian spacetime) and Lagrangian density (for Euclidean 4-space) that reflects the signature of the respective metric manifold.