Explicit Poincare embedding of the harmonic-oscillator model of composite elementary particles

There are two unitarily inequivalent realizations of the Poincar\'e Lie algebra of the recently proposed harmonic-oscillator model of elementary particles. One of these, which may be called the usual type, is trivial. The nature of the second type 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 Poincar\'e states with nontrivial internal structure.