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 ¿ (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 ¿-transformation, and fermion number conservation. In this way we connect W ¿ -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 ¿k (or ¿k ) 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.