Canonical quantization and the spectral action, a nice example
| dc.creator | Besnard, Fabien | |
| dc.date | 2007-02-08 | |
| dc.date | 2007-06-18 | |
| dc.date.accessioned | 2026-07-07T11:21:44Z | |
| dc.date.available | 2026-07-07T11:21:44Z | |
| dc.description | We study the canonical quantization of the theory given by Chamseddine-Connes spectral action on a particular finite spectral triple with algebra $M_2(\Cset)\oplus\Cset$. 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 both cases, but the gauge-invariance of the spectral action manifests itself by the presence of a non-trivial degeneracy structure for our distance operator. | |
| dc.description | A footnote on p 10 added wrt published version | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0702049 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0702049 | |
| dc.identifier | J.Geom.Phys.57:1757-1770,2007 | |
| dc.identifier | doi:10.1016/j.geomphys.2007.02.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/194350 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Operator Algebras | |
| dc.title | Canonical quantization and the spectral action, a nice example | |
| dc.type | text |