Overall, these web pages are a collection of material on treating General Relativity as a Quantum Field Theory. The material has been posted and maintained by John Donoghue.
The most recent set of lectures about GR as a QFT are those of the TRISEP school hosted at the Perimeter Institute in July 2018. I am giving 4.5 hours of lectures here to students who span the experimental and theoretical aspects of fundamental physics.
I am using this page to give the lecture notes and related materials for this course.
Lecture 1 Effective Field Theory Notes from the first class. The first class covered: Why do quantum calculations work?, the principles of EFT (locality, the energy expansion, matching/measuring), the linear sigma model, direct construction of the EFT, verification of the equivalence, EFT to one loop, renormalization, predictions and power counting. Video recording is here
Lecture 2 Gravity from a particle physics perspective ( Notes here) and the Background Field Method (Notes here) Higgs as mediator, need to use energy-momentum as source, energy-momentum from symmetry, gauge theory analogies for sources, gauging translation invariance, metric and its transformation, Success – energy momentum as source, covariant derivatives from symmetries, curvatures from covariant derivatives, actions for gravity, the weak field limit, gauge invariance and gauge fixing, the propagator, Feynman rules and ghost stories. For the background field method: Higgs example, QED example, general calculation of divergences, renormalizing the sigma model, comments about the heat kernel. Video recording is here
Lecture 3 Here are the notes from the third lecture. We covered: Rules of EFT, Scalar loop, background field expansion for GR, gauge fixing, deriving the ghost Lagrangian, graviton loop result, the effect of the local terms, the correction to the gravitational potential, unitarity techniques, light bending, graviton scattering, beyond scattering amplitudes, Barvinsky Vilkovisky, limits to the effective field theory, extreme IR limits. Video recording
Some exercises are found here.
Some pedagogic references:
The effective field theory treatment of quantum gravity. JFD – for those that know GR best but EFT less.
Introduction to the effective field theory description of gravity. JFD – for those who know EFT best but GR less.
Quantum gravity in everyday life: General relativity as an effective field theory Cliff Burgess – Living reviews
Appendix B of Dynamics of the Standard Model. This contains a description of the Heat Kernel method, and the renormalization of the chiral Lagrangian of QCD.
Feynman’s 1963 paper on the quantization of gravity . Fun to read!
Folks interested in more detail can access my EPFL lectures ( covering 14 hours total) from 2016. The notes can be accessed here. These have been written up and posted on the arXiv with the help of Mikhail Ivanov and Andrei Shkerin.
Finally I gave a semester-long course on this topic in 2015, and the notes are available here. ( Note that UMass has changed their cloud storage procedure, so that the video links do not presently work. I have the files saved and hope to re-post them using a different storage system.)