Diffeomorphism invariant quantum fields in perturbative algebraic quantum field theory

In this talk I discuss the notion of diffeomorphism invariant quantities in locally covariant quantum field theory. This is important especially in the context of quantum gravity. In the paper ''Batalin-Vilkovisky formalism in the functional approach to classical field theory'' of K. Fredenhagen and myself from 2011 we proposed to define diffeomorphism invariant classical fields with the use of a certain generalization of the Batalin-Vilkovisky formalism. Here I present a similar result which was obtained recently also for quantum fields.