Classical Electromagnetic Field Theory in the Presence of Magnetic Sources

Using two new well-defined four-dimensional potential vectors,we formulate the classical Maxwell field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources.We set up a consistent Lagrangian for the theory.Then from the action principle we obtain both Maxwell‘s equation and the equation of motion of a dyon moving in the electromagnetic field.