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

TL;DR

The paper proposes a concrete program to obtain the semiclassical limit of canonical Lorentzian quantum GR in 4D using graph-labeled coherent states on cotangent bundles over compact gauge groups and an Infinite Tensor Product extension to realize the thermodynamic limit. It develops kinematical coherent states peaked on classical data, constructs diffeomorphism-covariant approximate continuum operators from graph degrees of freedom, and introduces the ITP framework to handle infinite-volume physics and potential topology changes, linking to Fock-like structures in suitable sectors. It also provides a mechanism to optimize fluctuations by balancing Planck, mesoscopic, and macroscopic scales, suggesting that the continuum and classical limits merge in a controlled way, with explicit formulas for the optimal scales. The work lays the groundwork for connecting nonperturbative canonical quantum gravity to quantum field theory on curved spacetimes, extracting corrections to the Standard Model, and exploring RG-like behavior under diffeomorphism symmetry, culminating in a rigorous treatment of semiclassical states and thermodynamic limits in loop quantum gravity.

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.