Temporal Lorentzian Spectral Triples

Nicolas Franco
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