Noncommutative geometric spaces with boundary: Spectral action

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Chamseddine, Ali H.^2,3  Connes, Alain^1,3,4 

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

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

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

[4] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Noncommutative spaces with boundary;    Spectral action;    Standard model;   

DOI  :  10.1016/j.geomphys.2010.10.002

来源: Elsevier

【 摘 要 】

We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the hermiticity of the Dirac operator. We then define spectral triples of noncommutative spaces with boundary. In particular we evaluate the spectral action corresponding to the noncommutative space of the standard model and show that the Einstein-Hilbert action gets modified by the addition of the extrinsic curvature terms with the right sign and coefficient necessary for consistency of the Hamiltonian. We also include effects due to the addition of a dilaton field. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free