On the absence of localized curvature in the weak-coupling phase of quantum gravity

TL;DR

This paper investigates the weak-coupling phase of Euclidean quantum gravity, revealing a non-local behavior with no localized curvature in Wilson loops, and proposes a quantum formula for gravitational potential energy consistent with this vacuum structure.

Contribution

It demonstrates the absence of localized curvature in the weak-coupling phase and relates this to numerical results in quantum Regge Calculus, providing a new quantum formula for gravitational potential energy.

Findings

Wilson loops show no localized curvature at low temperature

The vacuum exhibits non-local behavior unlike usual gauge fields

Proposes a quantum formula for gravitational potential energy

Abstract

In the weak field expansion of euclidean quantum gravity, an analysis of the Wilson loops in terms of the gauge group, $SO(4)$, shows that the correspondent statistical system does not develope any configuration with localized curvature at low temperature. Such a ``non-local'' behavior contrasts strongly with that of usual gauge fields. We point out a possible relation between this result and those of the numerical simulations of quantum Regge Calculus. We also give a general quantum formula for the static potential energy of the gravitational interaction of two masses, which is compatible with the mentioned vacuum structure.