N.S.B. Letters NSBL-EP-018 The SU7 Structure of 18-Dimensional Unification

In an 18-dimensional gravidynamic unification model the spacetime and the internal symmetries of 4 generations of leptons and quarks are consolidated in a 256-component Majorana-Weyl-Dirac fermion. In such a framework, the dynamics of vector bosons as well as Higgs scalars would be generated at the quantum level through a unified coupling of an antisymmetric tensor of rank 3 to the fermions. We exhibit the complete U7 structure of the latter coupling. This extensive work begins by writing the Lorentz algebra of 18 dimensional spacetime in terms of its 4-dimensional Lorentz subalgebra and an internal O14 factor. The latter is expressed via its U7 subalgebra. The 256-component fermion is expressed in terms of 64 Weyl fermions, and their Dirac conjugates, in 4 dimensions. Likewise the 3rd rank antisymmetric tensor is expressed in terms of vectors and scalars in 4 dimensions. The emerging picture regarding the fundamental fermions, and their interactions, would lead to aspects that are well described by a complementing O14 and SU7 grand unification schemes.