An alternative model of particle physics in a 10-dimension (pseudo) Euclidian space-time

Abstract

A consistent description of the fundamental interactions of particle physics based upon the assumption of 6 real extra dimensions is presented. The usual 4-dimension space-time, a curved hypersurface with the Lorentz group as local symmetry, is assumed to be embedded in a larger flat 10-dimension space-time. Two additional assumptions are made: (i) the orthogonal 6-d space in any point of the hypersurface is invariant under the orthogonal group SO(6) or one of its subgroups, (ii) in that space only the invariant, or distinguished, subgroups of SO(6) can be symmetry groups for the physical states. There are only two such possibilities, each of them corresponding to one type of particles: (i) hadrons, experiencing a gauge field associated to a real symmetry group GH(6) , isomorphous to SU(3) and identified with the strong interaction, and (ii) leptons experiencing another gauge field associated with a real symmetry group GL(6), isomorphous to SU(2)xU(1) but different from the usual electro-weak coupling. Moreover both hadrons and leptons are subject to weak and electromagnetic interactions plus a scalar Higgs-type coupling. That description can be extended so as to include gravitation. Postulating a minimal Lagrangian in the full 10-dimension space-time leads to introduce one effective additional vector-type field, which does not act the same way upon hadrons and leptons, thus provoking an apparent violation of the equivalence principle.