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Exploring the Causal Structures of Almost Commutative Geometries
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra $\mathcal{S}(\mathbb{R}^{1,1}) \otimes M_2(\mathbb{C})$, which has a non-trivial space of internal degrees of freedom. It turns out that the causality condition imposes restrictions on the motion in the internal space. Moreover, we show that the requirement of causality favours a unitary evolution in the internal space.
Keywords: noncommutative geometry; causal structures; Lorentzian spectral triples. 
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     author = {Nicolas Franco and Micha{\l} Eckstein},
     title = {Exploring the {Causal} {Structures} of {Almost} {Commutative} {Geometries}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a9/}
}
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Nicolas Franco; Michał Eckstein. Exploring the Causal Structures of Almost Commutative Geometries. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a9/

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