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

Understand

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.