Selection Rules for Parafields and the Absence of Para Particles in Nature

Green's parafield quantization is reviewed. It is shown, both for a single field and for sets of fields, that all Fock-like representations of Green's trilinear commutation rules are realized by Green's ansatz with anticommuting (commuting) Bose (Fermi) component fields for para-Bose (para-Fermi) fields. Restrictions on the form of the interaction Hamiltonian density $H_I\mathrm{}\left(x\right)\mathrm{}$ are derived from the requirement that $H_I\mathrm{}\left(x\right)\mathrm{}$ be a paralocal operator. From these restrictions on $H_I$ selection rules on the $S$ matrix are proved to all orders of perturbation theory. The most important such rule prohibits all reactions in which the total number of para particles of order $p>\mathrm{}1\mathrm{}$ in the initial and final states is one. This last selection rule, together with experimental information, leads to the conclusion that no presently known particle can be para.