The 6j-symbol: Recursion, Correlations and Asymptotics

Abstract

We study the asymptotic expansion of the 6j-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up to the third order corrections beyond the leading order. Moreover, in the framework of spinfoam models for 3d quantum gravity, we show how these recursion relations can be used to derive Ward-Takahashi-like identities between the expectation values of graviton-like spinfoam correlations.

11 pages

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Cited by in corpus (16)

• The Spin Foam Approach to Quantum Gravity
• Diffeomorphisms in group field theories
• The Hamiltonian constraint in 3d Riemannian loop quantum gravity
• Dynamics for a 2-vertex Quantum Gravity Model
• Recurrence relations for spin foam vertices
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
• A new Hamiltonian for the Topological BF phase with spinor networks
• Pushing Further the Asymptotics of the 6j-symbol
• Generating Functions for Coherent Intertwiners
• Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: an Elementary Method
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• The new spin foam models and quantum gravity
• A New Recursion Relation for the 6j-Symbol
• Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions