Constraining the standard model with a supergroup

The author has introduced in this paper the conjecture that the δμ(2/1) superalgebra transitions relate particle fields to ghost fields, of the type introduced by Feynman, DeWitt, Faddeev and Popov to ensure the Unitarity of Quantized Gauge Theories. δμ(2/1) thus resembles the Becchi-Rouet-Stora and the Curci-Ferrari algebras, also relating particle and ghost fields, and providing algebraic shortcuts, simplifying the imposition of Unitarity throughout the renormalization procedure. However, the author has also noted that for the spin 1/2 (matter) fields, the grading of the carrier vector-spaces is correlated with chirality. Indeed, the author has proved elsewhere that the (reducible) matrices representing U(2)/sub w/ x SU(3)/sub color/, when acting on supermultiplets constructed from juxtapositions of independent matter multiplets and graded according to chirality (thus disregarding Lorentz invariance in that auxiliary construction) have vanishing supertraces. Coming back to the statistics of the submultiplets in the matter representations, the author notices that μ/sub q/ of equation is proportional to the helicities of the leptons whose (y, vertical bar i vertical bar, i/sub 3/) quantum numbers are given by the above representations. Thus, the grading in δμ(2/1) coincides with helicity. The left-handed leptons are assigned to (-1, 1/2+), the left-handed quarks to (1/3, 1/2/sup +/); their right-handed antiparticles belong to (1, 1/2/sup +/) and (-1/3,1/2/sup +/)