Inner fluctuations in noncommutative geometry without the first order condition

JOURNAL OF GEOMETRY AND PHYSICS

卷:73

Article

Chamseddine, Ali H.^1,3  Connes, Alain^2,3,4  van Suijlekom, Walter D.⁵ 

[1] Amer Univ Beirut, Dept Phys, Beirut, Lebanon

[2] Coll France, F-75005 Paris, France

[3] IHES, F-91440 Bures Sur Yvette, France

[4] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[5] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, NL-6525 AJ Nijmegen, Netherlands

关键词: Noncommutative geometry;    Spectral action;    Standard model;   

DOI  :  10.1016/j.geomphys.2013.06.006

来源: Elsevier

【 摘 要 】

We extend inner fluctuations to spectral triples that do not fulfill the first-order condition. This involves the addition of a quadratic term to the usual linear terms. We find a semi-group of inner fluctuations, which only depends on the involutive algebra A and which extends the unitary group of A. This has a key application in noncommutative spectral models beyond the Standard Model, of which we consider here a toy model. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free