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.Comment: 32 pages, revised Introduction, typos correcte
