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Exploring the Causal Structures of Almost Commutative Geometries
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Exploring the Causal Structures of Almost Commutative Geometries
Інший ID:
2010 Mathematics Subject Classification: 58B34; 53C50; 54F05
DOI:10.3842/SIGMA.2014.010
DOI:10.3842/SIGMA.2014.010
Посилання:
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.
Підтримка:
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.
Дата:
2014
Переглядів:
491
Завантажень:
206
Анотація:
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.
