Potential energy in quantum gravity

TL;DR

This paper derives a general, non-perturbative expression for the static gravitational potential energy between two masses in quantum gravity, analogous to Wilson loops in gauge theories, enabling numerical evaluation.

Contribution

It introduces a new formula for gravitational potential energy in quantum gravity using invariant vacuum expectation values, applicable in regularized Euclidean formulations.

Findings

Provides a non-perturbative expression for gravitational potential energy.

Establishes a gauge-invariant approach similar to Wilson loops.

Enables potential numerical simulations of quantum gravitational interactions.

Abstract

We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for functional integral formulations of euclidean quantum gravity, regularized to avoid conformal instability. It could be regarded as the analogue of the Wilson loop of gauge theories and allows in principle, through numerical lattice simulations or other approximation techniques, non perturbative evaluations of the potential or of the effective coupling constant.