  At the classical level, the SU(2/1) superalgebra offers a natural description
of the elementary particles: leptons and quarks massless states, graded by
their chirality, fit the smallest irreducible representations of SU(2/1). Our
new proposition is to pair the left/right space-time chirality with the
superalgebra chirality and to study the model at the one-loop quantum level.
If, despite the fact that they are non-Hermitian, we use the odd matrices of
SU(2/1) to minimally couple an oriented complex Higgs scalar field to the
chiral Fermions, novel anomalies occur. They affect the scalar propagators and
vertices. However, these undesired new terms cancel out, together with the
Adler-Bell-Jackiw vector anomalies, because the quarks compensate the leptons.
The unexpected and striking consequence is that the scalar propagator must be
normalized using the antisymmetric super-Killing metric and the scalar-vector
vertex must use the symmetric d_aij structure constants of the superalgebra.
Despite this extraordinary structure, the resulting Lagrangian is actually
Hermitian.
