Examples of non integer dimensional geometries
Mathematical Physics
2008-09-29 v2 High Energy Physics - Theory
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0809.4678,
title = {Examples of non integer dimensional geometries},
author = {R. Trinchero},
journal= {arXiv preprint arXiv:0809.4678},
year = {2008}
}
Comments
18 pages,4 figures