Maxwell-Lorentz Dynamics of Rigid Charges

We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We consider also a modified theory of electromagnetism where no self-fields occur. That theory and our results are crucial for approaching the as yet unsolved problem of the general existence of dynamics of Wheeler Feynman electromagnetism, which we shall address in the follow up paper.