Examples of non integer dimensional geometries

Details Examples of non integer dimensional geometries Examples of non integer dimensional geometries

2008-09-26

arxiv.org/abs/0809.4678v2

Physics

Mathematical Physics

18 pages,4 figures

Scientific paper

Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter dependent deformation of the canonical spectral triple over S1. Its dimension spectrum includes real non-integer values. It has a non-trivial differential algebra and in contrast with the one dimensional case there are no junk forms for a non-vanishing deformation parameter. The distance on this space depends non-trivially on this parameter.

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