Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry
摘要
We compute the metric associated to noncommutative spaces described by a tensor product of spectral triples. Well known results of the two-sheets model (distance on a sheet, distance between the sheets) are extended to any product of two spectral triples. The distance between different points on different fibres is investigated. When one of the triple describes a manifold, one find a Pythagorean theorem as soon as the direct sum of the internal states (viewed as projections) commutes with the internal Dirac operator. Scalar fluctuations yield a discrete Kaluza-Klein model in which the extra metric component is given by the internal part of the geometry. In the standard model, this extra component comes from the Higgs field.
引用
@article{arxiv.hep-th/0104108,
title = {Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry},
author = {P. Martinetti and R. Wulkenhaar},
journal= {arXiv preprint arXiv:hep-th/0104108},
year = {2009}
}
备注
References added. Argument in example of commutative spaces precised. Proposition 3 (very) slightly generalised