On the representations of Poincare group associated with unstable particles

The problem of relativistically-covariant description of unstable particles is reexamined. We follow the approach which associates a unitary reducible representation of Poincare group with a larger isolated system, and compare it with the one ascribing a non-unitary irreducible representation to the unstable particle alone. It is shown that the problem roots in choice of the subspace Hsub(u) of the state Hilbert space which could be related to the unstable particle. Translational invariance of Hsub(u) is proved to be incompatible with unitarity of the boosts. Further we propose a concrete choice of Hsub(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 a moving particle is obtained