The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity

TL;DR

This paper discusses issues in non-perturbative quantum gravity approaches, highlighting the absence of long-range correlations and unbounded energy, and proposes a new Hamiltonian constraint formulation to address these problems.

Contribution

It identifies fundamental problems in existing quantum gravity formulations and introduces a novel approach to the Hamiltonian constraint to potentially resolve them.

Findings

Existing approaches lack long-range correlations and massless particles.

The $ADM$ energy can be unbounded from below in these theories.

A new Hamiltonian constraint formulation is proposed to overcome these issues.

Abstract

It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states lack long ranged correlations, because the form of the state allows a division into spatial regions, such that no change in the physical state in one region can be measured by observables restricted to another. These disconnected regions have generically finite expectation value of physical volume, which means that the theory has no long ranged correlations or massless particles. One consequence of this is that the $ADM$ energy is unbounded from below, at least when that is defined with respect to a natural notion of quantum asymptotic flatness and a corresponding definition of an operator that measures $E_{ADM}$ (which is given here). These problems occur in Thiemann's new formulation of quantum gravity. Related issues arise in some other approaches such as that of Borissov, Rovelli and Smolin. A new approach to the Hamiltonian constraint, which may avoid the problem of the lack of long ranged correlations, is proposed.