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 electro-magnetic field.