A new SU(2/1) supergroup with determinant 1 explains many mysteries of the weak interactions

Abstract

Taken as a classification paradigm completing the standard model, a new compact form of the SU(2/1) supergroup explains many mysterious properties of the weak interactions: the maximal breaking of parity, the fractional charges of the quarks, the cancellation of the quantum field theory anomalies, and ties together the existence of the right neutrinos and of the heavier Fermions. This compact supergroup is constructed by exponentiating the matrices representing the leptons and the quarks which form a semi-direct sum of Kac modules of the real superalgebra su(2/1,R) such that the overall trace of the $U(1)$ weak-hypercharge $Y$ vanishes. Remarkably, all the elements of this supergroup have Berezinian 1 and determinant 1. In practice, $Tr(Y)=0$ simply means that the electric charge of the hydrogen atom is zero.