Duality Symmetry of Quantum Electrodynamics and Magnetic Charges

TL;DR

This paper investigates the duality symmetry in quantum electrodynamics (QED), revealing that what might appear as magnetic charges are actually electric charges and that true magnetic charges are incompatible with QED's gauge-field framework.

Contribution

The study introduces a dual gauge field and a symmetric Lagrangian to analyze duality in QED, concluding magnetic charges cannot exist within this theory.

Findings

Dual charges are identified as electric charges.

True magnetic charges are incompatible with QED.

No new conservation laws arise from duality symmetry.

Abstract

The duality symmetry between electricity and magnetism hidden in classical Maxwell equations suggests the existence of dual charges, which have usually been interpreted as magnetic charges and have not been observed in experiments. In quantum electrodynamics (QED), both the electric and magnetic fields have been unified into one gauge field, which makes this symmetry inconspicuous. Here, we recheck the duality symmetry of QED by introducing a dual gauge field and a dual symmetric Lagrangian. Within the framework of gauge-field theory, we show that the electric-magnetic duality symmetry cannot give any new conservation law. By checking the charge-charge interaction and the quantum Lorentz-force equation, we find that the introduced dual charges are electric charges, not magnetic charges. More importantly, we show that true magnetic charges are not compatible with the gauge-field theory of QED, because the interaction between a magnetic charge and an electric charge cannot be mediated via the exchange of gauge photons.