Noncommutative geometry, Lorentzian structures and causality

Nicolas Franco, Michał Eckstein

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)

Abstract

The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.
Original languageFrench
Title of host publicationMathematical Structures of the Universe
Place of PublicationKrakow
PublisherMichał Heller, Michał Eckstein, Sebastian Szybka
Pages315-340
EditionCopernicus Center Press
ISBN (Print)978-83-7886-107-2
Publication statusPublished - 11 Sep 2014

Cite this

Franco, N., & Eckstein, M. (2014). Noncommutative geometry, Lorentzian structures and causality. In Mathematical Structures of the Universe (Copernicus Center Press ed., pp. 315-340). Krakow: Michał Heller, Michał Eckstein, Sebastian Szybka.
Franco, Nicolas ; Eckstein, Michał. / Noncommutative geometry, Lorentzian structures and causality. Mathematical Structures of the Universe. Copernicus Center Press. ed. Krakow : Michał Heller, Michał Eckstein, Sebastian Szybka, 2014. pp. 315-340
@inbook{fba5073651ea47baa6fed190bdb45193,
title = "Noncommutative geometry, Lorentzian structures and causality",
abstract = "The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.",
author = "Nicolas Franco and Michał Eckstein",
year = "2014",
month = "9",
day = "11",
language = "Fran{\cc}ais",
isbn = "978-83-7886-107-2",
pages = "315--340",
booktitle = "Mathematical Structures of the Universe",
publisher = "Michał Heller, Michał Eckstein, Sebastian Szybka",
edition = "Copernicus Center Press",

}

Franco, N & Eckstein, M 2014, Noncommutative geometry, Lorentzian structures and causality. in Mathematical Structures of the Universe. Copernicus Center Press edn, Michał Heller, Michał Eckstein, Sebastian Szybka, Krakow, pp. 315-340.

Noncommutative geometry, Lorentzian structures and causality. / Franco, Nicolas; Eckstein, Michał.

Mathematical Structures of the Universe. Copernicus Center Press. ed. Krakow : Michał Heller, Michał Eckstein, Sebastian Szybka, 2014. p. 315-340.

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)

TY - CHAP

T1 - Noncommutative geometry, Lorentzian structures and causality

AU - Franco, Nicolas

AU - Eckstein, Michał

PY - 2014/9/11

Y1 - 2014/9/11

N2 - The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.

AB - The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.

M3 - Chapitre (revu par des pairs)

SN - 978-83-7886-107-2

SP - 315

EP - 340

BT - Mathematical Structures of the Universe

PB - Michał Heller, Michał Eckstein, Sebastian Szybka

CY - Krakow

ER -

Franco N, Eckstein M. Noncommutative geometry, Lorentzian structures and causality. In Mathematical Structures of the Universe. Copernicus Center Press ed. Krakow: Michał Heller, Michał Eckstein, Sebastian Szybka. 2014. p. 315-340