Duality symmetry of quantum electrodynamics and magnetic charges

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), the electric and magnetic fields are unified into a single gauge field, which makes this symmetry inconspicuous. Here, we revisit 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. Notably, we show that genuine magnetic charges are incompatible with the traditional QED gauge-field framework, as the interaction between a magnetic charge and an electric charge cannot be mediated via the exchange of gauge photons.