Irreducible representations of a parafield and the connection of the parafield with usual fields

All irreducible separable representations of the non-relativistic para-Fermi field of order 3 in the configuration space are considered. The existence of many different irreducible representations of the parafield permits us to interpret the excited states of this field as the states of particles with internal degrees of freedom. These states can be labelled by the Young patterns and the eigenvalues of internal quantum number like baryonic and hypercharges. The parafield theory is shown to be equivalent to the theory of three kinds of ordinary ferminons, like quarks, and one of them, ‘strange’, can be distinguished from the other two by means of its interaction, not only statistically but also dynamically. Thus the parafield theory is shown to be equivalent to some model of the physicalSU (3) symmetry of hadrons when the strong and medium-strong interactions could be switched on but the electromagnetic and weak interactions should be switched off.