Abstract
This paper is devoted to the study of the description of elementary physical systems interacting with an external constant electromagnetic field and the construction of their differential wave equations from a group-theoretical point of view. In this context certain local realizations of the Poincaré group are studied. The linearization of this problem is carried out by building the associated representation group that turns out to be the well-known Maxwell group. In this way the usual method (concerning local realizations) that has been employed in studying free systems to the interacting case is extended.
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