Dimensional reduction without continuous extra dimensions

Abstract

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. © 2013 American Institute of Physics.