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Abstract: We study recurrence relations for various Wigner 3nj-symbols and thenon-topological 10j-symbol. For the 6j-symbol and the 15j-symbols whichcorrespond to basic amplitudes of 3d and 4d topological spin foam models,recurrence relations are obtained from the invariance under Pachner moves andcan be interpreted as quantizations of the constraints of the underlyingclassical field theories. We also derive recurrences from the action ofholonomy operators on spin network functionals, making a more precise linkbetween the topological Pachner moves and the classical constraints.Interestingly, our recurrence relations apply to any SU2 invariant symbol,depending on the cycles of the corresponding spin network graph. Another methodis used for non-topological objects such as the 10j-symbol and pseudo-isoceles6j-symbols. The recurrence relations are also interpreted in terms ofelementary geometric properties. Finally, we discuss the extension of therecurrences to take into account boundary states which leads to equationssimilar to Ward identities for correlation functions in the Barrett-Cranemodel.

Autor: Valentin Bonzom, Etera R. Livine, Simone Speziale


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