Invariants of spin networks with boundary in Quantum Gravity and TQFT's

dc.creatorCarbone, Gaspare
dc.creatorCarfora, Mauro
dc.creatorMarzuoli, Annalisa
dc.date1999-05-20
dc.date.accessioned2026-07-07T03:33:12Z
dc.date.available2026-07-07T03:33:12Z
dc.descriptionThe 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.description9 pages
dc.identifierhttps://arxiv.org/abs/gr-qc/9905076
dc.identifierhttp://arxiv.org/abs/gr-qc/9905076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/36529
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleInvariants of spin networks with boundary in Quantum Gravity and TQFT's
dc.typetext

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