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Based upon a fundamental principle, the generalized gauge principle, we construct a general model with G(L) x G(R)' x Z(2) gauge symmetry, where Z(2) = pi(4)(G(L)) is the fourth homotopy group of the gauge group G(L), by means of the non-commutative differential geometry and reformulating the standard model with the Higgs field being a gauge field on the fourth homotopy group of their gauge groups. We show that in this approach not only the Higgs held is automatically introduced on an equal footing with ordinary Yang-Mills gauge potentials and there are no extra constraints among the parameters at the tree level but also most importantly the models survive quantum corrections.

The Standard Model with Higgs as Gauge Field on Fourth Homotopy Group