Duality in Off-Shell Electromagnetism

TL;DR

This paper explores the limitations of duality symmetry in off-shell electromagnetism and proposes a Clifford algebra extension, but finds it cannot explain the absence of magnetic monopoles.

Contribution

It demonstrates that the five-dimensional U(1) gauge theory lacks natural duality symmetry and introduces a Clifford algebra generalization to restore it.

Findings

Duality symmetry is broken in the five-dimensional theory.

Clifford algebra extension can restore duality symmetry.

The generalized framework does not explain the absence of magnetic monopoles.

Abstract

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five dimensional U(1) gauge theory associated with Stueckelberg-Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five dimensional theory prevents a natural generalization of the Dirac monopole, since the theory is not symmetric under duality transformations. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of a Clifford algebra. Nevertheless, the generalized framework does not permit us to recover the phenomenological (or conventional) absence of magnetic monopoles.