Representations of the Poincare group associated with unstable particles

The problem of a relativistically covariant description of unstable particles is reexamined. We follow the approach which associates a unitary reducible representation of the Poincare group with a larger isolated system, and compare it with the one ascribing a nonunitary irreducible representation to the unstable particle alone. It is shown that the problem originates in the choice of the subspace scrH/sub u/ of the state Hilbert space which could be related to the unstable particle. Translational invariance of scrH/sub u/ is proved to be incompatible with unitarity of the boosts. Further, we propose a concrete choice of scrH/sub u/ and argue that in most cases of the actual experimental arrangements this subspace is effectively one dimensional. A correct slow-down for decay of the moving particles is obtained