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Universe 2017, 3(1), 25; doi:10.3390/universe3010025

The Geometry of Noncommutative Spacetimes

1
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. prof. Stanisława Łojasiewicza 11, 30-348 Kraków, Poland
2
Copernicus Center for Interdisciplinary Studies, ul. Szczepańska 1/5, 31-011 Kraków, Poland
Academic Editors: Mariusz P. Dąbrowski, Manuel Krämer and Vincenzo Salzano
Received: 11 February 2017 / Revised: 10 March 2017 / Accepted: 12 March 2017 / Published: 16 March 2017
(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)
View Full-Text   |   Download PDF [286 KB, uploaded 17 March 2017]   |  

Abstract

We review the concept of ‘noncommutative spacetime’ approached from an operational stand-point and explain how to endow it with suitable geometrical structures. The latter involves i.a. the causal structure, which we illustrate with a simple—‘almost-commutative’—example. Furthermore, we trace the footprints of noncommutive geometry in the foundations of quantum field theory. View Full-Text
Keywords: Lorentzian geometry; causality; noncommutative geometry; quantum spacetime Lorentzian geometry; causality; noncommutative geometry; quantum spacetime
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Eckstein, M. The Geometry of Noncommutative Spacetimes. Universe 2017, 3, 25.

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