Electric-Magnetic Duality in Massless QED?

TL;DR

This paper explores a potential duality between standard and non-Hermitian QED, suggesting particles could carry both electric and magnetic charges, leading to a finite, scale-invariant quantum field theory with dyons.

Contribution

It proposes a duality between QED and magnetic QED, implying particles can have both electric and magnetic charges, and interprets the fine structure constant as a dyon charge quantization.

Findings

Particles can carry both electric and magnetic charges.

The theory predicts a finite, scale-invariant spectrum of dyons.

The fine structure constant relates to dyon charge quantization.

Abstract

The possibility that QED and recently developed non-Hermitian, or magnetic, versions of QED are equivalent is considered. Under this duality the Hamiltonians and anomalous axial currents of the two theories are identified. A consequence of such a duality is that particles described by QED carry magnetic as well as electric charges. The proposal requires a vanishing zero bare fermion mass in both theories; Dirac mass terms are incompatible with the conservation of magnetic charge much as Majorana masses spoil the conservation of electric charge. The physical spectrum comprises photons and massless spin-1/2 particles carrying equal or opposite electric and magnetic charges. The four particle states described by the Dirac fermion correspond to the four possible charge assignments of elementary dyons. This scale invariant spectrum indicates that the quantum field theory is finite. The Johnson Baker Willey eigenvalue equation for the fine structure constant in finite spinor QED is interpreted as a Dirac-like charge quantisation condition for dyons.