Duality Symmetry of Quantum Electrodynamics

Li-Ping Yang, Dazhi Xu

Published 2021-03-01Version 1

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 never been observed in experiments. In quantum electrodynamics (QED), both the electric and magnetic fields have been unified into one gauge field $A_{\mu}$, which makes this symmetry inconspicuous. Here, we recheck the duality symmetry of QED by introducing a dual gauge field. Within the framework of gauge-field theory, we first show that the electric-magnetic duality symmetry cannot give any new conservation law. By checking charge-charge interaction and specifically the quantum Lorentz force equation, we find that the dual charges are electric charges, not magnetic charges. More importantly, we show that true magnetic charges are not compatible to the gauge-field theory of QED, because the interaction between a magnetic charge and an electric charge can not be mediated by gauge photons.