Magnetic QED

TL;DR

This paper introduces a non-Hermitian quantum electrodynamics model describing magnetic monopoles, revealing unique properties such as parity-odd magnetic charge and attractive forces between like-charged monopoles, differing from standard QED.

Contribution

It presents a non-Hermitian formulation of QED for Dirac monopoles, including a detailed analysis of its Lorentz and parity properties and classical force calculations.

Findings

Like-charged monopoles attract in the weak coupling regime

Magnetic charge is parity-odd, unlike electric charge

Classical calculations confirm attractive forces between monopoles

Abstract

A non-Hermitian form of QED is presented which describes interacting Dirac monopoles. The theory is related by a canonical transformation to a model proposed by Milton. As in Hermitian QED an abelian gauge potential is coupled to a four-component fermion. Under proper Lorentz transformations and time-reversal the fermion field transforms like a Dirac spinor but has a non-standard parity transformation. This implements the property that magnetic charge, unlike electric charge, is parity-odd. A consequence of the non-Hermiticity is that there is an attractive force between identical charged particles, at least in the weakly coupled regime. This effect can be understood even at the classical level; a simple calculation of the force between classical Dirac monopoles is presented which shows that like charge monopoles attract and opposite charges repel.