A New Recursion Relation for the 6j-Symbol

Abstract

The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations. In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths. This article presents a new recursion formula for the square of the 6j-symbol. In the asymptotic regime, the new recursion is shown to characterize the closure of the relevant tetrahedron. Since the 6j-symbol is the basic building block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we also discuss how to generalize the method to derive more general recursion relations on the full amplitudes.

10 pages, v2: title and introduction changed, paper re-structured; Annales Henri Poincare (2011)

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Cited by in corpus (6)

• The Spin Foam Approach to Quantum Gravity
• Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint
• Bubble divergences and gauge symmetries in spin foams
• Generating Functions for Coherent Intertwiners
• Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
• Spinfoam tunneling of quantum geometries in angle variables