Particle multiplets in the Standard Model group particles under symmetry transformations of gauge groups.
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SUPPORTED
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refutedsupported
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Peer-reviewed literature demonstrates that particle multiplet structures in the Standard Model are assigned according to generator actions and representations of the relevant gauge groups.
Connections and Generalized Gauge Transformations
Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonlinear SU(4) action on an $S^7$ bundle is applied to the dimensional reduction of eleven-dimensional supergravity and ten-dimensional superstring theory to four dimensions. A principle, consistent with higher-dimensional superstring theory, is suggested to explain the types of gauge interactions that arise in the standard model based on the geometry of the internal symmetry spaces. It is shown why a Lie group structure is required for vector bosons in pure gauge theories and that the application of division algebras to force unification must begin with the fermions comprising the elementary particle multiplets of the standard model. A suggestion is made for establishing a mechanism for the cancellation of anomalies within this approach to superstring theory.
Published as: Int.J.Geom.Meth.Mod.Phys. 2 (2005) 505
arXiv categories: hep-th
An alternative formulation of SU(3)c x SU(2)L, x U(1)y of the standard model is presented in which four extra complex Grassmann coordinates are appended to space-time coordinates. The three families of leptons and quarks are imbedded in the fermionic sector of an overall bosonic superfield and the Higgs fields are imbedded in the Lorentz scalar sector of the superfield. The SU(3) SU(2)L, x U(1) y multiplet structure can be assigned to the component fields by introducing the corresponding generators acting in Grassmann space and the V ‚ÄövÑvÆ A structure of the weak current turns out as the result of the minimal fermionic representation. The particle multiplets are anomaly-free but not asymptotically free due to extra exotic states. The Yukawa interaction appears from the trilinear interaction of the master superfield, but the spontaneously symmetry breaking cannot be reproduced from the analogous quartic super-Higgs potential. Unfortunately, the resulting mass spectrum of the standard particles (quarks and leptons) cannot be reconciled with the experimental results. However the standard SU(3) x SU(2) x U(1) gauge interaction can be reproduced for the minimal gauge group. The 'extended' gauge group includes leptoquarks as well as interfamilial interactions.
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