Renata Ferrero: Relational Observables in Asymptotically Safe Gravity

One of the greatest issues for a quantum theory of gravitation is how to generalise the notion of local observable quantities. A viable approach is to construct a physical local reference frame and give physical meaning to the components of any tensor evaluated in this frame: all measurements of tensor or scalar fields can be thought of as relational observables. The lack of observables is a major critique of the current Asymptotic Safety program. However, in the last years, within the functional renormalisation group framework an equation to evaluate the flow and the scaling dimension of composite operators has been developed. Relational observables are therefore natural candidates for composite operators. We introduce an approach to compute the renormalisation group flow of relational observables in quantum gravity which evolve from their microscopic expressions towards the full quantum expectation value. These methods can be applied to a large class of relational observables within a derivative expansion for different physical coordinate systems. Based on arXiv:2112.02118.