Three-particle poincaré states and SU(6) × SU(3) as a classification group for baryons

A complete set of democratic quantum numbers is introduced to classify the states of an irreducible unitary representation (IUR) of the Poincaré group obtained from the decomposition of the direct product of three IUR. Such states are identified with the baryon states constituted of three free relativistic quarks. The transformation from current to constituent quarks is then easily reobtained. Moreover, the group SU(6) × SU(3) appears naturally as a collinear classification group for baryons. Results similar to those of the symmetric harmonic oscillator quark model are obtained.