Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model

TL;DR

This paper demonstrates how to compute geometric quantities in 3D quantum gravity using grasping rules, analyzing the classical limit and quantum corrections of the volume of a tetrahedron in the Ponzano-Regge model.

Contribution

It introduces explicit methods for calculating geometrical expectation values and explores the semiclassical limit and quantum corrections in the Ponzano-Regge model.

Findings

Large spin expansion dominated by classical volume

Quantum corrections identified at next-to-leading order

Explicit computation of tetrahedron volume using grasping rules

Abstract

We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin expansion of this value is dominated by the classical expression, and we study the next to leading order quantum corrections.