Abstract
Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these theories. In this work the extended class of irreducible representations with positive `mass' parameter is explicitly determined. Several new representations in such extension, so far excluded, give rise to consistent theories for Klein-Gordon particles and also to new species of particle theories.
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