Quaternionic Grassmannian SU(4) × SU(4) Grand Unified Theory

Abstract

An SU(4) × SU(4) Grand Unified Theory incorporating known leptons and colored quarks into a common multiplet representation utilizing a set of four (4) anticommuting Grassmann toordinates appended to space-time coordinates and field states expressed in quaternion form is presented. Two sets of SU(4) generators, one in terms of Grassmannian coordinates and their partial derivatives while the other in terms of quaternion imaginaries, were used to portray SU(4) × SU(4) gauge symmetry of the theory. Electromagnetic, strong nuclear interactions of fermions as well as weak interaction of a left-handed type covering three generations of the particle spectrum were generated.