Dimensional Reduction without Extra Continuous Dimensions
  We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and generalized connections associated with the "geometry" of space-times with discrete extra dimensions. We apply our formalism to theories of gauge- and gravitational fields and find natural geometrical origins for an axion- and a dilaton field, as well as a Higgs field. 
Ali Chamseddine, Juerg Froehlich, Baptiste Schubnel, Daniel Wyler
math-ph hep-th math.MP