# Temporal Lorentzian Spectral Triples

September 02, 2014

We present the notion of temporal Lorentzian spectral triple which is an
extension of the notion of pseudo-Riemannian spectral triple with a way to
ensure that the signature of the metric is Lorentzian. A temporal Lorentzian
spectral triple corresponds to a specific 3+1 decomposition of a possibly
noncommutative Lorentzian space. This structure introduces a notion of global
time in noncommutative geometry. As an example, we construct a noncommutative
Minkowsky spacetime with the use of a degenerate Moyal product.

open access link
Rev. Math. Phys., Vol. 26, No. 8, 1430007 (2014)

@article{Franco:2012ga,
author = "Franco, Nicolas",
title = "{Temporal Lorentzian Spectral Triples}",
journal = "Rev. Math. Phys.",
volume = "26",
year = "2014",
number = "08",
pages = "1430007",
doi = "10.1142/S0129055X14300076",
eprint = "1210.6575",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1210.6575;%%"
}

Keywords:

noncommutative geometry, Lorentzian geometry, spectral triples