Finite-Range Electromagnetic Interaction and Magnetic Charges: Spacetime Algebra or Algebra of Physical Space?

TL;DR

This paper develops a finite-range electromagnetic theory with electric and magnetic charges using spacetime algebra and algebra of physical space, highlighting the advantages of the APS formalism for geometric interpretation.

Contribution

The paper formulates a new finite-range EM theory with magnetic charges in both STA and APS formalisms, favoring APS for its geometric interpretation capabilities.

Findings

Both STA and APS are equally effective in formulating the model.

APS formalism allows a geometric interpretation of the imaginary unit.

The theory maintains Lorentz, gauge, and duality invariances.

Abstract

A new finite-range electromagnetic (EM) theory containing both electric and magnetic charges constructed using two vector potentials A^{} and Z^{} is formulated in the spacetime algebra (STA) and in the algebra of the three-dimensional physical space (APS) formalisms. Lorentz, local gauge and EM duality invariances are discussed in detail in the APS formalism. Moreover, considerations about signature and dimensionality of spacetime are discussed. Finally, the two formulations are compared. STA and APS are equally powerful in formulating our model, but the presence of a global commuting unit pseudoscalar in the APS formulation and the consequent possibility of providing a geometric interpretation for the imaginary unit employed throughout classical and quantum physics lead us to prefer the APS approach.