Causality in noncommutative two-sheeted space-times

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 details 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.

26 pages, 2 figures

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Cited by in corpus (10)

• The Lorentzian distance formula in noncommutative geometry
• Causality for nonlocal phenomena
• The noncommutative geometry of Zitterbewegung
• Metrics and causality on Moyal planes
• Lorentzian fermionic action by twisting euclidean spectral triples
• Noncommutative geometrical origin of the energy-momentum dispersion relation
• Families of spectral triples and foliations of space(time)
• Quantum causality constraints on kappa-Minkowski space-time
• Quantum causality in $\kappa$-Minkowski and related constraints
• Physical models from noncommutative causality