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A general technique is presented for constructing a quantum theory of afinite number of interacting particles satisfying Poincar\'e invariance,cluster separability, and the spectral condition. Irreducible representationsand Clebsch-Gordan coefficients of the Poincar\'e group are the centralelements of the construction. A different realization of the dynamics isobtained for each basis of an irreducible representation of the Poincar\'egroup. Unitary operators that relate the different realizations of the dynamisare constructed. This technique is distinguished from other solutions of thisproblem because it does not depend on the kinematic subgroups of Dirac's formsof dynamics. Special basis choices lead to kinematic subgroups.Comment: 50 pages - replacement - new title and stylistic changes consistent  with published versio

Cluster properties in relativistic quantum mechanics of N-particle systems