NONCOMMUTATIVE GEOMETRY AND GRADED ALGEBRAS IN ELECTROWEAK INTERACTIONS

The Standard Model of Electroweak Interactions can be described by a generalized Yang-Mills field incorporating both the usual gauge bosons and the Higgs fields. The graded derivative by means of which the Yang-Mills field strength is constructed involves both a differential acting on space-time and a differential acting on an associative graded algebra of matrices. The square of the curvature for the corresponding covariant derivative yields the bosonic Lagrangian of the Standard Model. We show how to recover the whole fermionic part of the Standard Model in this framework. Quarks and leptons fit naturally into the smallest typical and nontypical irreducible representations of the graded …