Causality in noncommutative two-sheeted space-times

Nicolas Franco; Michał Eckstein

doi:10.1016/j.geomphys.2015.05.008

Causality in noncommutative two-sheeted space-times

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is given in detail when the sheet is a 2- or 4-dimensional globally hyperbolic spin manifold. The conclusions are then generalised to a point-dependent distance between the two sheets resulting from the fluctuations of the Dirac operator.

Original language	English
Pages (from-to)	42-58
Number of pages	17
Journal	Journal of Geometry and Physics
Volume	96
Early online date	6 Jun 2015
DOIs	https://doi.org/10.1016/j.geomphys.2015.05.008
Publication status	Published - 1 Oct 2015
Externally published	Yes

Keywords

Causal structures
Lorentzian spectral triples
Noncommutative geometry

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10.1016/j.geomphys.2015.05.008

http://arxiv.org/abs/1502.04683

Cite this

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abstract = "We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is given in detail when the sheet is a 2- or 4-dimensional globally hyperbolic spin manifold. The conclusions are then generalised to a point-dependent distance between the two sheets resulting from the fluctuations of the Dirac operator.",

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AB - We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is given in detail when the sheet is a 2- or 4-dimensional globally hyperbolic spin manifold. The conclusions are then generalised to a point-dependent distance between the two sheets resulting from the fluctuations of the Dirac operator.

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Causality in noncommutative two-sheeted space-times

Abstract

Keywords

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