Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model
| dc.creator | Kramer, P. | |
| dc.creator | Lorente, M. | |
| dc.date | 2008-04-25 | |
| dc.date | 2008-04-30 | |
| dc.date.accessioned | 2026-07-07T09:35:46Z | |
| dc.date.available | 2026-07-07T09:35:46Z | |
| dc.description | In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each face of a triangle the spherical function constructed from the Dolginov-Biedenharn function. In part II we apply the same technique to the Lorentz invariant state sum model. We need three new ingredients: the classification of the edges and the corresponding subspaces that arises in the simplicial decomposition, the irreps of SL(2,C) and its isomorphism to the bivectors appearing in the 4-simplices, the need of a zonal spherical function from the intertwining condition of the tensor product for the simple representations attached to the faces of the simplicial decomposition. | |
| dc.description | LaTex 19 pages | |
| dc.identifier | https://arxiv.org/abs/0804.4162 | |
| dc.identifier | http://arxiv.org/abs/0804.4162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159942 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model | |
| dc.type | text |