Asymptotics of 4d spin foam models

TL;DR

This paper analyzes the asymptotic behavior of four-dimensional spin foam models, revealing their semi-classical limits relate closely to Regge calculus for certain boundary data.

Contribution

It provides the first detailed asymptotic analysis of 4d spin foam models, connecting their boundary data to Regge action in semi-classical regimes.

Findings

Asymptotic formulas relate to Regge action

Semi-classical limits are established for multiple models

Boundary data influence asymptotic behavior

Abstract

We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry.