Fock representation for quaternion fields

A Fock representation is determined for a nonrelativistic self-adjoint (“Majorana”) field based on quaternions, and the quantum mechanics of the parafermions of third order corresponding to it is formulated. Attention is drawn to the difference between the gauge “pseudocolor” $SO(3)$ symmetry of the automorphisms of such a field and the global $SU(3)$ symmetry of the states of the particles corresponding to it in the Fock space.