کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896968 | 1044472 | 2007 | 14 صفحه PDF | دانلود رایگان |
We study the canonical quantization of the theory given by Chamseddine–Connes spectral action on a particular finite spectral triple with algebra M2(C)⊕CM2(C)⊕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.
Journal: Journal of Geometry and Physics - Volume 57, Issue 9, August 2007, Pages 1757–1770