Towards testing the Fr\"ohlich-Morchio-Strocchi mechanism in quantum gravity

TL;DR

This paper explores the potential application of the Fr"ohlich-Morchio-Strocchi mechanism to quantum gravity, aiming to understand how diffeomorphism-invariant operators can be used to test quantum gravity theories.

Contribution

It proposes extending a known mechanism from flat-space quantum field theory to the context of quantum gravity, suggesting possible testing methods like dynamical triangulation.

Findings

The mechanism could be applicable to quantum gravity.

Dynamical triangulation may serve as a testing method.

Provides a framework for diffeomorphism-invariant observables.

Abstract

Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite. This makes an evaluation in general involved, even if the concrete implementation of quantum gravity should be treatable (semi-)perturbatively in general. A mechanism developed by Fr\"ohlich, Morchio and Strocchi for flat-space-time quantum field theory may also be applicable in this case. It may be possible to test this mechanism with methods like dynamical triangulation.