Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
arXiv:0802.3983 · doi:10.1016/j.nuclphysb.2008.05.012
Abstract
We consider an exact expression for the 6j-symbol for the isosceles tetrahedron, involving integrals over SU(2), and use it to write the two-point function of 3d gravity on a single tetrahedron as a group integral. The perturbative expansion of this expression is then performed with respect to the boundary geometry using a simple saddle-point analysis. We derive the complete expansion in inverse powers of the length scale and evaluate explicitly the quantum corrections up to second order. Finally, we use the same method to provide the complete expansion of the isosceles 6j-symbol with the explicit phases at all orders and the next-to-leading correction to the Ponzano-Regge asymptotics.
16 pages, 3 figs, revtex4, a numerical coefficient corrected in eq (60)
References in corpus (12)
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- The loop-quantum-gravity vertex-amplitude
- Flipped spinfoam vertex and loop gravity
- The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
- The complete LQG propagator: II. Asymptotic behavior of the vertex
- Linearized dynamics from the 4-simplex Regge action
- Spin foam model from canonical quantization
- Numerical evidence of regularized correlations in spin foam gravity
- The perturbative Regge-calculus regime of Loop Quantum Gravity
- Coherent states, constraint classes, and area operators in the new spin-foam models
- Numerical indications on the semiclassical limit of the flipped vertex