Quaternion gauge fields. Pseudocolor

A simplified Gyunaydin–Gyursey model, in which a Majorana field constructed using quaternions combines a lepton and a color quark, is considered. Formulation of the gauge principle directly in the quaternions leads to the appearance of two vector quaternion gauge fields, these corresponding to the decomposition $SO(4)\simeq SO(3)\times SO(3)$ of the invariance group. The diagonal subgroup $SO(3)$ of automorphisms of the quaternions appears as a pseudocolor symmetry of the quarks, and the gauge fieldcorresponding to it as the field of three color gluons. The other gauge field corresponds to lepton-quark transitions and in the presence of spontaneous breaking of the $SO(4)$ gauge symmetry by the scalar quaternion field acquires a (large) finite mass.