We consider Maxwell-Lorentz dynamics: this is to say, Newton law under theView original: http://arxiv.org/abs/1201.5685
action of a Lorentz force which obeys Maxwell equations. A natural class of
solutions are those given by lagrangian submanifolds of the phase space when it
is endowed with the symplectic structure modified by the electromagnetic field.
We have found that the existence of this type of solution leads us directly to
the Klein-Gordon equation as a compatibility condition.