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June 2011 Large-spin asymptotics of Euclidean LQG flat-space wavefunctions
Aleksandar Miković, Marko Vojinović
Adv. Theor. Math. Phys. 15(3): 801-847 (June 2011).

Abstract

We analyze the large-spin asymptotics of a class of spin-network wavefunctions of Euclidean loop quantum gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an amplitude for a spin network whose graph is a composition of the wavefunction spin network graph with the dual one-complex graph and the tetrahedron graphs for a triangulation of the spatial 3-manifold. This spin-network amplitude can be represented as a product of $6j$ symbols, which is then used to find the large-spin asymptotics of the wavefunction. By using the Laplace method we show that the large-spin asymptotics is given by a sum of Gaussian functions. However, these Gaussian functions are not of the type, which gives the correct graviton propagator.

Citation

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Aleksandar Miković. Marko Vojinović. "Large-spin asymptotics of Euclidean LQG flat-space wavefunctions." Adv. Theor. Math. Phys. 15 (3) 801 - 847, June 2011.

Information

Published: June 2011
First available in Project Euclid: 11 June 2012

zbMATH: 1257.83015
MathSciNet: MR2929690

Rights: Copyright © 2011 International Press of Boston

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Vol.15 • No. 3 • June 2011
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