On the definition of spacetimes in noncommutative geometry: Part I

JOURNAL OF GEOMETRY AND PHYSICS

卷:123

Article

Besnard, Fabien¹  Bizi, Nadir² 

[1] EPF, Pole Rech ML Paris, 3 Bis Rue Lakanal, F-92330 Sceaux, France

[2] Univ Pierre & Marie Curie Paris 06, Sorbonne Univ, IRD UMR 206,Museum Natl Hist Nat, UMR CNRS 7590,Inst Mineral Phys Mat & Cosmochim, 4 Pl Jussieu, F-75005 Paris, France

关键词: Noncommutative geometry;    Clifford algebras;    Spin geometry;    Noncommutative geometry;   

DOI  :  10.1016/j.geomphys.2017.09.008

来源: Elsevier

【 摘 要 】

In this paper we consider semi-Riemannian time and space oriented manifolds of even dimension, and characterize the Lorentzian and antilorentzian signatures in terms of a time-orientation 1-form and a natural Krein product on spinor fields. It turns out that all the data available in Noncommutative Geometry (the algebra of functions, the Krein space of spinor fields, the representation of the algebra on it, the Dirac operator, charge conjugation and chirality), but nothing more, play a role in this characterization. It thus yields a possible definition extending Connes' notion of even spectral triple to the Lorentzian setting. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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