Quantum gravity asymptotics from the SU(2) 15j symbol

Abstract

The asymptotics of the SU(2) 15j symbol are obtained using coherent states for the boundary data. The geometry of all non-suppressed boundary data is given. For some boundary data, the resulting formula is interpreted in terms of the Regge action of the geometry of a 4-simplex in 4-dimensional Euclidean space. This asymptotic formula can be used to derive and extend the asymptotics of the spin foam amplitudes for quantum gravity models. The relation of the SU(2) Ooguri model to these quantum gravity models and their continuum Lagrangians is discussed.

approx 17 pages

References in corpus (11)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Flipped spinfoam vertex and loop gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Area-angle variables for general relativity
• Quantum geometry from phase space reduction
• Holomorphic Factorization for a Quantum Tetrahedron
• Asymptotic analysis of the Ponzano-Regge model for handlebodies

Cited by in corpus (46)

• The Spin Foam Approach to Quantum Gravity
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• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• SU(2) graph invariants, Regge actions and polytopes
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Coarse graining free theories with gauge symmetries: the linearized case
• Gluing polyhedra with entanglement in loop quantum gravity
• A proposed proper EPRL vertex amplitude
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• A spin-foam vertex amplitude with the correct semiclassical limit
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• Numerical analysis of spin foam dynamics and the flatness problem
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
• Asymptotics of 4d spin foam models
• On the exact evaluation of spin networks
• Quantum Spacetime on a Quantum Simulator
• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• On the Expansions in Spin Foam Cosmology
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• The Construction of Spin Foam Vertex Amplitudes
• Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: an Elementary Method
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Numerical evaluation of spin foam amplitudes beyond simplices
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• The Barrett-Crane model: asymptotic measure factor
• The new spin foam models and quantum gravity
• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity
• State Sums and Geometry
• A New Recursion Relation for the 6j-Symbol
• Corrigendum: The Plebanski sectors of the EPRL vertex
• Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
• Geometry from local flatness in Lorentzian spin foam theories
• A Monte Carlo algorithm for spin foam intertwiners
• Generating Functionals for Spin Foam Amplitudes
• Cosmological states in loop quantum gravity on homogeneous graphs
• Effective geometry of Bell-network states on a dipole graph
• A saddle-point finder and its application to the spin foam model