Nonlocal correlations for semiclassical states in loop quantum gravity

TL;DR

This paper analyzes the two-point correlation functions of area operators in loop quantum gravity's semiclassical states, revealing short-range correlations in standard states and potential for long-range correlations in perturbed states, aligning with perturbative quantum gravity.

Contribution

It introduces a new class of semiclassical states with perturbations that can exhibit long-range correlations, bridging nonperturbative and perturbative quantum gravity insights.

Findings

Standard coherent states show exponential decay of correlations.

Perturbed states can display long-range correlations.

Some states reproduce graviton-like correlation decay.

Abstract

We compute the two-point correlation function of the area operator for semiclassical states of loop quantum gravity in the limit of large spins. The cases of intrinsic and extrinsic coherent states are considered, along with a new class of semiclassical states constructed as perturbations of Livine-Speziale coherent states. For the usual coherent states, the correlations are shown to be short-ranged, decaying exponentially with the distance. Introducing perturbations given by correlated elementary excitations and decays of the gravitational field along pairs of loops, we obtain new states that, while preserving the peakedness properties of the unperturbed states, can also display long-ranged correlations. The perturbed coherent states include examples reproducing the typical decay of correlations for quantum fluctuations of the geometry associated with free gravitons on a background metric. Such a behavior is a natural requirement for the compatibility of semiclassical states in quantum gravity with the physical regime pictured by perturbative quantum gravity.