P000084
How Clifford's chirality allows to extend the concepts of connection and curvature and the quantum analysis of gauge anomalies to the case of a Lie-Kac SU(2/1) superalgebra describing leptons and quarks.
*Jean Thierry-Mieg (NCBI, National Library of Medicine, National Institutes of Health, Bethesda, Maryland, USA)
The weak interactions are chiral. Experimentally, all left Fermions couple to the SU(2) weak isospin whereas all right Fermions are SU(2) neutral. The Lie-Kac SU(2/1) superalgebra offers a natural description of this assymetry since leptons and quarks graded by chirality fit its smallest irreducible representations. We show for the first time how chirality allows to construct an intrinsic geometrical connection form respecting the superalgebraic Bianchi identity without using Grassman numbers, then how the quantum field theory of this superconnection is induced by the Fermion loops, and finally how the cancellation of a new class of scalar anomalies induces a quantum superalgebraic minimal coupling involving the super-Killing metric and the symmetric structure constants of the superalgebra. At the foundation of this algebraic and geometrical model, the pairing of the Clifford chirality with the charge chirality of the superalgebra implements the Charge-Parity CP invariance of the weak interactions.