Particles within extended-spin space: Lagrangian connection

A spin-space extension is reviewed, which provides information on the standard model. Its defining feature is a common matrix space that describes symmetries and representations, and leads to limits on these, for given dimension. The model provides additional information on the standard model, whose interpretation requires an interactive formulation. Within this program, we compare the model's lepton-W generated interactive Lagrangian in (5+1)-dimensions, and that of the standard model. We derive the conditions for this matching, which apply to other Lagrangian terms. We also discuss the advantages of this extension, as compared to others.