New incorporation of generation mixing into the reconstruction of the standard model in NCG

The new scheme of NCG on the discrete space M4xZ2 is presented to incorporate the generation mixing the fermions into the generalized gauge field. Thus, the generalized gauge field contains the ordinary gauge field and the Higgs boson field together with the generation mixing matrix. This is similar result to that in formulations of Connes and others. However, in this formulation of NCG, the Higgs quartic coupling constant becomes non-zero even in one generation of fermion because one-form base dxμ and χ are adopted to describe the generalized gauge field instead of γμ and γ5