Statistical geometry of random weave states

TL;DR

This paper introduces a novel approach to constructing semiclassical states in quantum gravity by applying statistical geometry techniques to random spin networks, enabling the calculation of their geometric contributions.

Contribution

It pioneers the integration of classical statistical geometry with quantum spin network states to develop semiclassical states in non-perturbative quantum gravity.

Findings

Development of methods for constructing semiclassical states

Application of statistical geometry to spin networks

Calculation of area and volume contributions from random networks

Abstract

I describe the first steps in the construction of semiclassical states for non-perturbative canonical quantum gravity using ideas from classical, Riemannian statistical geometry and results from quantum geometry of spin network states. In particular, I concentrate on how those techniques are applied to the construction of random spin networks, and the calculation of their contribution to areas and volumes.