On the semiclassical limit of 4d spin foam models

TL;DR

This paper investigates the semiclassical behavior of 4d Riemannian spin foam models, showing that amplitudes align with classical geometry and Regge calculus, with the Immirzi parameter's influence vanishing in the limit.

Contribution

It demonstrates that spin foam amplitudes recover classical geometric actions in the semiclassical limit, clarifying the role of the Immirzi parameter.

Findings

Amplitudes are exponentially suppressed unless they correspond to a discrete geometry.

When geometric, amplitudes match the exponential of i times the Regge action.

Dependence on the Immirzi parameter disappears in the semiclassical limit.

Abstract

We study the semiclassical properties of the Riemannian spin foam models with Immirzi parameter that are constructed via coherent states. We show that in the semiclassical limit the quantum spin foam amplitudes of an arbitrary triangulation are exponentially suppressed, if the face spins do not correspond to a discrete geometry. When they do arise from a geometry, the amplitudes reduce to the exponential of i times the Regge action. Remarkably, the dependence on the Immirzi parameter disappears in this limit.