| The gauge symmetries provide the Standard Model, and it involves a Spontaneous Symmetry Breakdown (SSB), which is called the Higgs Mechanism. However, the geometrical formulation that can include the SSB and the unification of gauge groups have not solved yet. In order to solve these problems, we pay attention to two geometrical tools, that is, the superconnection and Noncommutative Geometry (NCG). And we consider the supergroup SU(2/1) as a candidate of the electroweak unification group. The SU(2/1) unification model was formulated with several geometrical frameworks, mainly, superconnection and the Mainz Marseille (MM) version of NCG. On the other hand, the Connes Lott (CL) model with 'original' NCG was suggested without the supergroup SU(2/1). In these models the Higgs scalar field can be geometrically formulated. In this dissertation we attempt the new Ne'eman Fairlie SU(2/1) model in the geometrical framework of the CL model. By assuming the 3 3 lepton and 4 4 quark representations of SU(2/1) in the generalized one form, we construct the Standard Model of one fermionic generation. |
