The Laplace Transform of Quantum Gravity

TL;DR

This paper explores a novel mathematical relationship between Einstein gravity and its strong coupling regime using Laplace transforms, revealing a diffusion process in the space of three-metrics related to spacetime volume.

Contribution

It introduces a Laplace transform framework connecting different regimes of quantum gravity and proposes a diffusion equation governing the Feynman propagator in the strong coupling limit.

Findings

Gravity regimes are related via Laplace transform.

Feynman propagator satisfies a diffusion equation in three-metric space.

Spacetime volume acts as an evolution parameter.

Abstract

Following analogies with relativistic point particles, and Schild strings, we show that the Einstein gravity and its strong coupling regime (or the Planck mass going to 0) are related to each other through a Laplace transform. The Feynman propagator of gravity in the strong coupling regime satisfies a functional diffusion equation in the three-metric space with the evolution parameter being the volume of spacetime. We conjecture that the relationship between both regimes is consistent with the existence of an evolution operator in which time is replaced by the volume of spacetime