2016/03/22 by Kasia Rejzner
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Covariant transformation #Diffeomorphism #General covariance #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Hořava–Lifshitz gravity #Infinitesimal #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Observable #Quantum field theory #Quantum gravity #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1142/s0218271816300123
16 pages, based on a plenary talk given at the 14th Marcel Grossmann Meeting in Rome (July 2015)
arxiv created 2016/03/22 · openalex publication_date 2016/04/01 · arxiv updated 2016/04/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Perturbative algebraic quantum field theory (pAQFT) is a mathematically rigorous framework that allows to construct models of quantum field theories (QFTs) on a general class of Lorentzian manifolds. Recently, this idea has been applied also to perturbative quantum gravity (QG), 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 paper, I will outline a general framework that allows to quantize theories with local symmetries (this includes infinitesimal diffeomorphism transformations) with the use of the Batalin–Vilkovisky (BV) formalism. This approach has been successfully applied to effective QG in a recent paper by Brunetti, 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.