Extended Chamseddine–fröhlich Approach to Noncommutative Geometry and the Two-Doublets Higgs Model

Abstract

The Chamseddine–Fröhlich approach to noncommutative geometry is extended by the introduction of the strong interaction sector in the mathematical formalism, and generalization of the Dirac operator and scalar product. This new approach is applied to the reformulation of the two-doublets Higgs model where the fuzzy mass, coupling and unitarity relations as well as mixing angles are derived. These tree level relations are no more preserved under the renormalization group flow in the context of the standard quantization method.

Towards a construction of the Dirac operator in the E6 Wulkenhaar's non commutative geometry

“…One takes into account from the bigining the spontaneous breakdown of the symmetry which is the case of models constructed by Chamseddine, Felder and Frolich [1]- [3] and authors in refs. [4]- [5]. The other does not take into account any breakdown of the symmetry in the definition of the L cycle and illustrated by the Wulkenhaar's models [7]- [8] and authors in refs.…”