Invariants of spin networks with boundary in Quantum Gravity and TQFT's
| dc.creator | Carbone, Gaspare | |
| dc.creator | Carfora, Mauro | |
| dc.creator | Marzuoli, Annalisa | |
| dc.date | 1999-05-20 | |
| dc.date.accessioned | 2026-07-07T03:33:12Z | |
| dc.date.available | 2026-07-07T03:33:12Z | |
| dc.description | The search for classical or quantum combinatorial invariants of compact n-dimensional manifolds (n=3,4) plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition function proposed by Ponzano and Regge to the case of a compact 3-dimensional simplicial pair $(M^3, \partial M^3)$. The resulting state sum $Z[(M^3, \partial M^3)]$ contains both Racah-Wigner 6j symbols associated with tetrahedra and Wigner 3jm symbols associated with triangular faces lying in $\partial M^3$. The analysis of the algebraic identities associated with the combinatorial transformations involved in the proof of the topological invariance makes it manifest a common structure underlying the 3-dimensional models with empty and non empty boundaries respectively. The techniques developed in the 3-dimensional case can be further extended in order to deal with combinatorial models in n=2,4 and possibly to establish a hierarchy among such models. As an example we derive here a 2-dimensional closed state sum model including suitable sums of products of double 3jm symbols, each one of them being associated with a triangle in the surface. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/gr-qc/9905076 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/9905076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/36529 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Invariants of spin networks with boundary in Quantum Gravity and TQFT's | |
| dc.type | text |