Positivity of relativistic spin network evaluations
| dc.creator | Pfeiffer, Hendryk | |
| dc.date | 2002-11-29 | |
| dc.date | 2004-01-02 | |
| dc.date.accessioned | 2026-07-07T03:27:21Z | |
| dc.date.available | 2026-07-07T03:27:21Z | |
| dc.description | Let G be a compact Lie group. Using suitable normalization conventions, we show that the evaluation of GxG-symmetric spin networks is non-negative whenever the edges are labeled by representations of the form V\otimes V^* where V is a representation of G, and the intertwiners are generalizations of the Barrett--Crane intertwiner. This includes in particular the relativistic spin networks with symmetry group Spin(4) or SO(4). We also present a counterexample, using the finite group S_3, to the stronger conjecture that all spin network evaluations are non-negative as long as they can be written using only group integrations and index contractions. This counterexample applies in particular to the product of five 6j-symbols which appears in the spin foam model of the S_3-symmetric BF-theory on the two-complex dual to a triangulation of the sphere S^3 using five tetrahedra. We show that this product is negative real for a particular assignment of representations to the edges. | |
| dc.description | 15 pages, LaTeX2e, 8 figures | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0211106 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0211106 | |
| dc.identifier | Adv.Theor.Math.Phys. 6 (2002) 827-846 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/34403 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Positivity of relativistic spin network evaluations | |
| dc.type | text |