Modified reconstruction of standard model in non-commutative differential geometry

Sogami recently proposed the new idea to express Higgs particle as a kind of gauge particle by prescribing the generalized covariant derivative with gauge and Higgs fields operating on quark and lepton fields. The field strengths for both the gauge and Higgs fields are defined by the commutators of the covariant derivative by which he could obtain the Yang-Mills Higgs Lagrangian in the standard model. Inspired by Sogami's work, we present a modification of our previous scheme to formulate the spontaneously broken gauge theory in non-commutative geometry on the discrete space M4xZ2 by introducing the generation mixing matrix K in dx operation on the fields ai(x, y) which compose the gauge and Higgs fields. The standard model is reconstructed according to the modified scheme, which does not yield not only any special relations between the particle masses but also the special restriction on the Higgs potential. (author)