Spin Foam Models of n-dimensional Quantum Gravity and Non-Archimedean and Non-Commutative Formulations
| dc.creator | Garcia-Islas, J. Manuel | |
| dc.date | 2004-01-13 | |
| dc.date.accessioned | 2026-07-07T03:28:23Z | |
| dc.date.available | 2026-07-07T03:28:23Z | |
| dc.description | This paper is twofold. First of all a complete unified picture of $n$-dimensional quantum gravity is proposed in the following sense: In spin foam models of quantum gravity the evaluation of spin networks play a very important role. These evaluations correspond to amplitudes which contribute in a state sum model of quantum gravity. In \cite{fk}, the evaluation of spin networks as integrals over internal spaces was described. This evaluation was restricted to evaluations of spin networks in $n$-dimensional Euclidean quantum gravity. Here we propose that a similar method can be considered to include Lorentzian quantum gravity. We therefore describe the the evaluation of spin networks in the Lorentzian framework of spin foam models. We also include a limit of the Euclidean and Lorentzian spin foam models which we call Newtonian. This Newtonian limit was also considered in \cite{jm}. Secondly, we propose an alternative formulation of spin foam models of quantum gravity with its corresponding evaluation of spin networks. This alternative formulation is a non-archimedean or $p$-adic spin foam model. The interest on this description is that it is based on a discrete space-time, which is the expected situation we might have at the Planck length; this description might lead us to an alternative regularisation of quantum gravity. Moreover a non-commutative formulation follows from the non-archimedean one. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0401058 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0401058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/34812 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Spin Foam Models of n-dimensional Quantum Gravity and Non-Archimedean and Non-Commutative Formulations | |
| dc.type | text |