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

New representations of Poincar\'e group for consistent Relativistic Particle Theories