Noncommutative Geometry and a Discretized Version of Kaluza-Klein Theory   with a Finite Field Content
  We consider a four-dimensional space-time supplemented by two discrete points assigned to a $Z_2$ algebraic structure and develop the formalism of noncommutative geometry. By setting up a generalised vielbein, we study the metric structure. Metric compatible torsion free connection defines a unique finite field content in the model and leads to a discretized version of Kaluza-Klein theory. We study some special cases of this model that illustrate the rich and complex structure with massive modes and the possible presence of a cosmological constant. 
Nguyen Ai Viet, Kameshwar C. Wali (Physics Department, Syracuse U.)