Matter and electromagnetic fields: remarks on the dualistic and unitarian standpoints

The study of the relation of matter and the electromagnetic field is a classical, intriguing problem both from physical and mathematical point of view. This relation can be interpreted from two different standpoints which, following [M. Born and L. Infeld, Foundations of the new field theory , Proc. Roy. Soc. London Ser. A 144 (1934), 425–451], are called unitarian standpoint and dualistic standpoint . In this paper we briefly describe two models which are related to the unitarian and the dualistic standpoint respectively. For each model it is possible to prove the existence of solitary waves which can be interpreted as matter particles