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A consistent description of the fundamental interactions of particle physicsbased upon the assumption of 6 real extra dimensions is presented. The usual4-dimension space-time, a curved hypersurface with the Lorentz group as localsymmetry, 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 pointof the hypersurface is invariant under the orthogonal group SO(6) or one of itssubgroups, (ii) in that space only the invariant, or distinguished, subgroupsof SO(6) can be symmetry groups for the physical states. There are only twosuch 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 groupGL(6), isomorphous to SU(2)xU(1) but different from the usual electro-weakcoupling. Moreover both hadrons and leptons are subject to weak andelectromagnetic interactions plus a scalar Higgs-type coupling. Thatdescription can be extended so as to include gravitation. Postulating a minimalLagrangian in the full 10-dimension space-time leads to introduce one effectiveadditional vector-type field, which does not act the same way upon hadrons andleptons, thus provoking an apparent violation of the equivalence principle.

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