Scalars Fields in the Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory

In this book we construct the Nonsymmetric Jordan–Thiry Theory unifying N.G.T. the Yang–Mills’ field the Higgs’ fields and scalar forces in a geometric manner. In this way we get masses from higher dimensions. We discuss spontaneous symmetry breaking the Higgs’ mechanism and a mass generation in the theory. The scalar field Ψ (as in the classical Jordan–Thiry Theory) is connected to the effective gravitational constant. This field is massive and has Yukawa-type behaviour. We discuss the rela- tion between R+ invariance and U(1)F from G.U.T. within Einstein λ-transformation and fermion number conservation. In this way we connect W μ -field from N.G.T. with a gauge field AF from G.U.T. We derive the equation of motion for a test particle from conservation laws in the hydrodynamic limit. We consider a truncation procedure for a tower of massive ρk (or Ψk ) scalar fields using Friedrichs’ theory and an approximation procedure for the lagrangian involving Higgs’ field . The geodetic equations on the Jordan–Thiry manifold are considered with an emphasis to terms involving Higgs’ field.