Quantum gravity in terms of topological observables

TL;DR

This paper reformulates four-dimensional quantum gravity as a topological quantum field theory, enabling perturbative analysis without breaking covariance and linking the partition function to topological invariants.

Contribution

It introduces a new perturbative framework for quantum gravity based on topological observables, with a dimensionless coupling constant and a novel expression for the generating functional.

Findings

Partition function expressed as expectation value of topological observable

Coupling constant becomes extremely small, enabling perturbation theory

Framework maintains general covariance in quantum gravity analysis

Abstract

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely small 10^{-120}. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory.