The Standard Model and the Generalized Covariant Derivative
نویسنده
چکیده
The generalized covariant derivative, that uses both scalar and vector bosons, is defined. It is shown how a grand unified theory of the Standard Model can be constructed using a generalized Yang-Mills theory. 1 The generalized covariant derivative Last year the authors developed a generalized Yang-Mills theory (GYMT) that used a covariant derivative that included not only vector bosons but scalar fields as well. [1], [2] The motivation at the time was to simplify the writing of the multiple terms of the Glashow-Weinberg-Salam (GWS) model using U(3). Our inspiration was an old idea by Fairlie and Ne’eman. [3] The idea is that the Higgs bosons fit neatly in the adjoint of SU(2/1), along with the gauge vector bosons, and that the hypercharges of the leptons are given correctly by one of the diagonal generators of that graded group. This model has two main problems, reviewed by us. [1] We then proposed that the problems of the old model could be resolved if one switched to the U(3) Lie group, since it is possible to obtain the correct quantum numbers for all the particles of the GWS if instead of the usual Gell-Mann representation a different one is used. This new representation is a linear combination of generators of the usual one. In this model an extra scalar boson makes its appearance, but it decouples from all the other particles. Here we study the application of a GYMT to the building of a grand unified theory (GUT) of the Standard Model at the rank 5 level. It turns out that, at this rank, there is only one possible GUT, and it is based on the group SU(6). The grand unification group has to contain two SU(3)’s, one to represent flavordynamics and another to represent chromodynamics. The algebra of SU(6) has SU(3)⊗ SU(3)⊗ U(1) as the group associated with one of its maximal subalgebras. It turns out that this group
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