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.

21 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

References in corpus (5)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• Towards Spinfoam Cosmology
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• The Ponzano-Regge model

Cited by in corpus (19)

• A Short Review of Loop Quantum Gravity
• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• The End of a Black Hole's Evaporation -- Part I
• A high-performance code for EPRL spin foam amplitudes
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Discrete gravity dynamics from effective spin foams
• Numerical analysis of spin foam dynamics and the flatness problem
• The End of a Black Hole's Evaporation -- Part II
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• From spin foams to area metric dynamics to gravitons
• 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