Geometrical unification of gauge and Higgs fields

Abstract

A geometrical unification of gauge and Higgs fields is suggested in a high-dimensional framework. The internal dimensions characterise the gauge group as a manifold; as a result of gauge invariance they do not appear in the Lagrangian. The inhomogeneous transformation behaviour of the physical Higgs field and the gauge field under gauge transformations is derived from the same principle; the actual differences in the transformation behaviour are attributed to the geometrical structure of the high-dimensional space. Mass spectra originate in the known dependence of gauge and Higgs fields on the internal coordinates. An explicit model is given where the gauge group is SU(2) and the Higgs field is in the adjoint representation and proposals are made for more general models. The model given here is equivalent to the corresponding hidden gauge symmetry model. Moreover, the Higgs mass and self-coupling of the Higgs field are predicted in terms of the vector boson mass and self-coupling of the gauge field respectively.