Exploratory applications of the Fr\"ohlich-Morchio-Strocchi mechanism in quantum gravity

A manifestly diffeomorphism-invariant approach to canonical quantum gravity requires to use composite operators. These can be considered to be bound states of matter and/or gravitons, intrinsically non-perturbative objects. An analytical approach to determine the properties of such bound states could be the Fr\"ohlich-Morchio-Strocchi mechanism. We explore the necessary technology by applying it to various $n$-point functions, including geon propagators and black-hole-particle vertices.