Strongly Decaying Particles and Relativistic Invariance

Before the discovery of strongly decaying particles ("resonances"), it was a good approximation to consider that all elementary particles are elementary systems, i.e., that their states transform according to an irreducible representation of the Poincaré group. This approximation is not valid for the strongly decaying particles, because they have a mass spectrum which cannot be neglected. To treat these particles on the same footing as the stable (or metastable) ones, one has to give a new definition of an elementary system. We describe the consequences of this definition for the one-particle states. The representation is no longer irreducible, but is multiplicity-free. The mass is a superselection rule; the states are described by density matrices, or better, by characteristic functions, defined on the Poincaré group. Specific examples are discussed ($\rho$ and $\omega$ mesons); the relevance of the new concepts introduced here for the quantum field theory of strong interactions is mentioned.