Effective quantum gravity observables and locally covariant QFT

TL;DR

This paper discusses a rigorous framework for defining and quantizing observables in effective quantum gravity using perturbative algebraic QFT and the BV formalism, ensuring background independence and diffeomorphism invariance.

Contribution

It introduces a general framework for quantizing theories with local symmetries, including diffeomorphisms, using the BV formalism within pAQFT, applied to effective quantum gravity.

Findings

Successfully applied BV formalism to quantum gravity

Proved perturbative background independence

Constructed diffeomorphism-invariant observables

Abstract

Perturbative algebraic quantum field theory (pAQFT) is a mathematically rigorous framework that allows to construct models of quantum field theories on a general class of Lorentzian manifolds. Recently this idea has been applied also to perturbative quantum gravity, treated as an effective theory. The difficulty was to find the right notion of observables that would in an appropriate sense be diffeomorphism invariant. In this article I will outline a general framework that allows to quantize theories with local symmetries (this includes infinitesimal diffeomorphism transformations) with the use of the BV (Batalin-Vilkovisky) formalism. This approach has been successfully applied to effective quantum gravity in a recent paper by R. Brunetti, K. Fredenhagen and myself. In the same paper we also proved perturbative background independence of the quantized theory, which is going to be discussed in the present work as well.