Asymptotics of Relativistic Spin Networks

Abstract

The stationary phase technique is used to calculate asymptotic formulae for SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the Spin Network evaluation. Finally we discuss the asymptotics of the SO(3,1) 10j-symbol.

31 pages, latex. v3: minor clarifications

References in corpus (1)

• Asymptotics of 10j symbols

Cited by in corpus (87)

• The Spin Foam Approach to Quantum Gravity
• Spin Foam Models for Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• Asymptotic analysis of the EPRL four-simplex amplitude
• On the semiclassical limit of 4d spin foam models
• Graviton propagator from background-independent quantum gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Spin Foams and Canonical Quantization
• Asymptotics of 10j symbols
• Group Integral Techniques for the Spinfoam Graviton Propagator
• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Cosmological Deformation of Lorentzian Spin Foam Models
• Linearized dynamics from the 4-simplex Regge action
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• SU(2) graph invariants, Regge actions and polytopes
• Quantum gravity asymptotics from the SU(2) 15j symbol
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Generalized Spinfoams
• Towards the graviton from spinfoams: higher order corrections in the 3d toy model
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• Semiclassical Mechanics of the Wigner 6j-Symbol
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• Coarse graining of spin net models: dynamics of intertwiners
• Semiclassical analysis of Wigner $3j$-symbol
• Recurrence relations for spin foam vertices
• Numerical evidence of regularized correlations in spin foam gravity
• Critical Overview of Loops and Foams
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• A spin-foam vertex amplitude with the correct semiclassical limit
• Discrete gravity dynamics from effective spin foams
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• A semiclassical tetrahedron
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• LQG propagator: III. The new vertex
• The Feynman propagator for spin foam quantum gravity
• Bubble divergences and gauge symmetries in spin foams
• Classical general relativity as BF-Plebanski theory with linear constraints
• Asymptotics of the Wigner 9j symbol
• Coupling gauge theory to spinfoam 3d quantum gravity
• Asymptotic analysis of the Ponzano-Regge model for handlebodies
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Semiclassical regime of Regge calculus and spin foams
• Testing the imposition of the Spin Foam Simplicity Constraints
• Pushing Further the Asymptotics of the 6j-symbol
• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• The Complete Barrett-Crane Model and its Causal Structure
• Spin-Foam Models and the Physical Scalar Product
• Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model
• The 6j-symbol: Recursion, Correlations and Asymptotics
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
• Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Recoupling coefficients and quantum entropies
• Symplectic and Semiclassical Aspects of the Schläfli Identity
• On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. II. Spin foam representation
• Spinfoams: Foundations
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• The Barrett-Crane model: asymptotic measure factor
• The new spin foam models and quantum gravity
• (2+1)-dimensional quantum gravity, spin networks and asymptotics
• Finiteness and Dual Variables for Lorentzian Spin Foam Models
• A More Sensitive Lorentzian State Sum
• A New Recursion Relation for the 6j-Symbol
• On the volume conjecture for classical spin networks
• Evaluation of new spin foam vertex amplitudes
• Rigorous construction of a Spin Foam Model for Lorentzian BF theory and Gravity: The foundations
• Relating Spin Foams and Canonical Quantum Gravity: A Discrete Step Evolution Formulation of Spin Foams
• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. I. BF Yang-Mills representation
• Reality Conditions for Spin Foams
• A look at area Regge calculus
• Ashtekar Formulation with Temporal Foliations
• Spin Foams for the Real, Complex Orthogonal Groups in 4D and the bivector scalar product reality constraint
• Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
• Polyhedra in spacetime from null vectors
• Spin Foam Models of Gravity and BF Theory as evolution of Spin Networks
• Hessian in the spinfoam models with cosmological constant
• Spin Foams for the SO(4,C) BF theory and the SO(4,C) General Relativity
• A Note on the Asymptotic Limit of the Four Simplex