Abstract

Preceded by a historical introduction the problem of a multi-dimensional extension of the geometrical framework of physical reality is discussed. Both metrical space-time and superspace are taken into account. Arguments in favour of a six-dimensional space-time D=6 are presented. A conviction that - according to „the spirit of Kaluza's theory” - all vector fields should be incorporated into the metric is a prejudice: some are ingredients of metric, but some other are genuine multivectors. The idea of supersymmetry is taken into account only in so far that fundamental fields form a supermultiplet of highest extension N=8, but supersymmetry is only global whereas local interactions do not need to be fully supersymmetric but locally gauge invariant and generally relativistic (replacing partial by covariant derivatives). Even a global supersymmetry may soften convergence difficulties so that super-string may be dispensed with. The set of all fields including 3 families of quarks and leptons may be arranged into a table resembling Mendelejev's one. A generalized Higgs mechanism explains high value of masses, also that of top quark