Exploring the Causal Structures of Almost Commutative Geometries

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 S(R¹,¹)⊗M₂(C), which has a non-trivial space of internal degrees of freedom. It turns out that the causality condition...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2014
Main Authors: Franco, N., Eckstein, M.
Format: Article
Language:English
Published: Інститут математики НАН України 2014
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146845
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Exploring the Causal Structures of Almost Commutative Geometries / N. Franco, M. Eckstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 28 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Franco, N.
Eckstein, M.
author_facet Franco, N.
Eckstein, M.
citation_txt Exploring the Causal Structures of Almost Commutative Geometries / N. Franco, M. Eckstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 28 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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 S(R¹,¹)⊗M₂(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.
first_indexed 2025-11-26T14:35:15Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-26T14:35:15Z
publishDate 2014
publisher Інститут математики НАН України
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spelling Franco, N.
Eckstein, M.
2019-02-11T17:08:13Z
2019-02-11T17:08:13Z
2014
Exploring the Causal Structures of Almost Commutative Geometries / N. Franco, M. Eckstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 28 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 58B34; 53C50; 54F05
DOI:10.3842/SIGMA.2014.010
https://nasplib.isofts.kiev.ua/handle/123456789/146845
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 S(R¹,¹)⊗M₂(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.
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
 honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
 This work was supported by a grant from the John Templeton Foundation.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Exploring the Causal Structures of Almost Commutative Geometries
Article
published earlier
spellingShingle Exploring the Causal Structures of Almost Commutative Geometries
Franco, N.
Eckstein, M.
title Exploring the Causal Structures of Almost Commutative Geometries
title_full Exploring the Causal Structures of Almost Commutative Geometries
title_fullStr Exploring the Causal Structures of Almost Commutative Geometries
title_full_unstemmed Exploring the Causal Structures of Almost Commutative Geometries
title_short Exploring the Causal Structures of Almost Commutative Geometries
title_sort exploring the causal structures of almost commutative geometries
url https://nasplib.isofts.kiev.ua/handle/123456789/146845
work_keys_str_mv AT francon exploringthecausalstructuresofalmostcommutativegeometries
AT ecksteinm exploringthecausalstructuresofalmostcommutativegeometries