Causality in noncommutative two-sheeted space-times
arXiv:1502.04683 · doi:10.1016/j.geomphys.2015.05.008
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
References in corpus (6)
- Particle Physics from Almost Commutative Spacetimes
- Equivariant Lorentzian Spectral Triples
- The noncommutative geometry of Zitterbewegung
- Noncommutative geometry, Lorentzian structures and causality
- The disappearance of causality at small scale in almost-commutative manifolds
- Lorentzian approach to noncommutative geometry