Canonical quantization and the spectral action; a nice example

JOURNAL OF GEOMETRY AND PHYSICS

卷:57

Article

Besnard, Fabien

关键词: noncommutative geometry;    spectral triples;    quantization;   

DOI  :  10.1016/j.geomphys.2007.02.007

来源: Elsevier

【 摘 要 】

We study the canonical quantization of the theory given by Chamseddine-Connes spectral action oil a particular finite spectral triple with algebra M-2(C) circle plus C. We define a quantization of the natural distance associated with this noncommutative space and show that the quantum distance operator has a discrete spectrum. We also show that it would be the same for any other geometric quantity. Finally we propose a physical Hilbert space for the quantum theory. This spectral triple had been previously considered by Rovelli as a toy model, but with a different action which was not gauge invariant. The results are similar in the two cases, but the gauge invariance of the spectral action manifests itself by the presence of a non-trivial degeneracy structure for our distance operator. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free