An SU(4) Grassmannian model for particles

An alternative formulation of SU(3)c x SU(2)L, x U(1)y of the standard model is presented in which four extra complex Grassmann coordinates are appended to space-time coordinates. The three families of leptons and quarks are imbedded in the fermionic sector of an overall bosonic superfield and the Higgs fields are imbedded in the Lorentz scalar sector of the superfield. The SU(3) SU(2)L, x U(1) y multiplet structure can be assigned to the component fields by introducing the corresponding generators acting in Grassmann space and the V ‚ÄövÑvÆ A structure of the weak current turns out as the result of the minimal fermionic representation. The particle multiplets are anomaly-free but not asymptotically free due to extra exotic states. The Yukawa interaction appears from the trilinear interaction of the master superfield, but the spontaneously symmetry breaking cannot be reproduced from the analogous quartic super-Higgs potential. Unfortunately, the resulting mass spectrum of the standard particles (quarks and leptons) cannot be reconciled with the experimental results. However the standard SU(3) x SU(2) x U(1) gauge interaction can be reproduced for the minimal gauge group. The 'extended' gauge group includes leptoquarks as well as interfamilial interactions.