Explicit Poincaré Embedding of the Harmonic-Oscillator Model of Composite Elementary Particles

There are two unitarily inequivalent realizations of the Poincare Lie algebra of the rescently propossed harmonic-osciliator model of elementary particles. One of these, which may be called the usual types, is trivial. The nature of the second types of realization, in which the structural information carried by continuous internal variables is not lost, suggests a very general method for avoiding the pitfalls suggested by the analyses of Wigner and O'Raifeartaigh for the construction of Poincare states with nontrivial internal structure. (auth)