Relation to existing constructions

Relational constructions and second-order expansions are already part of perturbative gravitational field theory BFHPR,Frob. In particular, Fröb computed gauge-invariant one-loop scalar correlation functions and exhibited cancellation between gauge-dependent self-energy contributions and relational corrections Frob. Neither the existence of relational observables nor the existence of such a cancellation is claimed as a new result here.

The locally covariant, renormalized Batalin–Vilkovisky treatment provides a framework for perturbative effective gravity BFR. It does not, by citation alone, establish the Ward identity of a newly specified boundary prescription or its compatibility with a fixed compact switch.

Hack treats the linearized Einstein–Klein–Gordon system on on-shell backgrounds Hack. Our background specialization is $(\eta ,0)$. The nonlinear coefficient problem studied below is not a linearization about a fixed nonzero scalar on Minkowski spacetime.

Retarded products and the Action Ward Identity are developed in DF. The Action Ward Identity concerns the dependence on local functionals rather than their density representatives. It must not be confused with a proved anomaly-free diffeomorphism Ward identity for the composite considered here.