Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension

TL;DR

This paper presents a new approach using graph-labelled coherent states and an Infinite Tensor Product extension to rigorously analyze the semi-classical limit of canonical quantum general relativity in four dimensions.

Contribution

It introduces a novel set of graph-labelled coherent states and an ITP extension of the Hilbert space to study the semi-classical limit.

Findings

Rigorous formulation of the infinite volume limit

New coherent states for quantum gravity

Extension of Hilbert space via ITP

Abstract

We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far.