Abstract
We consider an internal space of two discrete points in the fifth dimension of the Kaluza–Klein theory by using the formalism of noncommutative geometry — developed in a previous paper1 — of a spacetime supplemented by two discrete points. With the non-vanishing internal torsion two-form there are no constraints implied on the vielbeins. The theory contains a pair of tensor fields, a pair of vector fields and a pair of scalar fields. Using the generalized Cartan structure equation we are able to uniquely determine not only the Hermitian and metric-compatible connection one-forms, but also the nonvanishing internal torsion two-form in terms of vielbeins. The resulting action has a rich and complex structure, a particular feature being the existence of massive modes. Thus the nonvanishing internal torsion generates a Kaluza–Klein type model with zero and massive modes.
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