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Perturbative algebraic quantum field theory (pAQFT) is a mathematicallyrigorous framework that allows to construct models of quantum field theories ona general class of Lorentzian manifolds. Recently this idea has been appliedalso to perturbative quantum gravity, treated as an effective theory. Thedifficulty was to find the right notion of observables that would in anappropriate sense be diffeomorphism invariant. In this article I will outline ageneral framework that allows to quantize theories with local symmetries (thisincludes infinitesimal diffeomorphism transformations) with the use of the BV(Batalin-Vilkovisky) formalism. This approach has been successfully applied toeffective quantum gravity in a recent paper by R. Brunetti, K. Fredenhagen andmyself. In the same paper we also proved perturbative background independenceof the quantized theory, which is going to be discussed in the present work aswell.

Effective quantum gravity observables and locally covariant QFT