Searching for classical geometries in spin foam amplitudes: a numerical method

Abstract

We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano-Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude with three vertices. We study the summation over bulk spins, and we identify the stationary phase points that dominate it and that correspond to classical geometries. We complement with the numerical analysis of a four vertex transition amplitude and with a modification of the model that includes local curvature. We discuss the generalization of our results to the four-dimensional EPRL spin foam model, and we provide suggestions for new computations.

arXiv comment21 pages, 40 figures, prepared for the Focus Issue on "Numerical Investigations in Non-Perturbative Quantum Gravity" published in "Classical and Quantum Gravity". V2 updates: Section 5 has been updated with a new numerical algorithm and the preprint now matches with the published version

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Cited by in corpus (21)

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• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
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• Numerical analysis of spin foam dynamics and the flatness problem
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• From spin foams to area metric dynamics to gravitons
• Primordial fluctuations from quantum gravity
• Towards effective actions for the continuum limit of spin foams
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Numerical evaluation of spin foam amplitudes beyond simplices
• Curvature effects in the spectral dimension of spin foams
• Tunneling of quantum geometries in spinfoams
• Geometry from local flatness in Lorentzian spin foam theories
• Spinfoam tunneling of quantum geometries in angle variables
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling