Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-03-23
Class.Quant.Grav.26:155014,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
66 pages, approx. v2: minor corrections and significant improvements in presentation
Scientific paper
10.1088/0264-9381/26/15/155014
The definition of the Ponzano-Regge state-sum model of three-dimensional quantum gravity with a class of local observables is developed. The main definition of the Ponzano-Regge model in this paper is determined by its reformulation in terms of group variables. The regularisation is defined and a proof is given that the partition function is well-defined only when a certain cohomological criterion is satisfied. In that case, the partition function may be expressed in terms of a topological invariant, the Reidemeister torsion. This proves the independence of our definition on the triangulation of the 3-manifold and on those arbitrary choices made in the regularisation. A further corollary is that when the observable is a knot, the partition function (when it exists) can be written in terms of the Alexander polynomial of the knot. Various examples of observables in the three-sphere are computed explicitly. Alternative regularisations of the Ponzano-Regge model by the simple cutoff procedure and by the limit of the Turaev-Viro model are discussed, giving successes and limitations of these approaches.
Barrett John W.
Naish-Guzman Ileana
No associations
LandOfFree
The Ponzano-Regge model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Ponzano-Regge model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Ponzano-Regge model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-528835