Dimensional Reduction without Extra Continuous Dimensions

Details Dimensional Reduction without Extra Continuous Dimensions Dimensional Reduction without Extra Continuous Dimensions

2012-01-12

arxiv.org/abs/1201.2661v1

Physics

Mathematical Physics

21 pages

Scientific paper

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.

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