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

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.