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.

Using a weak deformation parameter approximation of paraquantum systems,, the Hamiltonian of the harmonic oscillator is studied and the eigenfunctions as well as the eigenvalues are derived.

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A noncommutative gauge model is constructed within the Frohlich-Chamssedine approach. The scalar, charged and neutral gauge boson masses as well as the new mixing angles are derived.