Exploring the Causal Structures of Almost Commutative Geometries

Nicolas Franco; Michał Eckstein

doi:10.3842/SIGMA.2014.010

Exploring the Causal Structures of Almost Commutative Geometries

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Résumé

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.

langue originale	Français
Nombre de pages	23
journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	10
Numéro de publication	010
Les DOIs	https://doi.org/10.3842/SIGMA.2014.010
Etat de la publication	Publié - 28 janv. 2014

mots-clés

noncommutative geometry
causal structures

Accès au document

10.3842/SIGMA.2014.010

http://arxiv.org/abs/1310.8225

Contient cette citation

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title = "Exploring the Causal Structures of Almost Commutative Geometries",

abstract = "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.",

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