  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.
