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. There are several sets of lectures and related material to be found on these pages.

The most recent set of lectures about GR as a QFT are those for the 2019 Nordic Winter School hosted north of Oslo in January. Embrace the winter! This consists of 4 hour-long lectures on EFT and General Relativity.

I am using this page to post the lecture notes and related materials for this course.

If you want more material than these notes provide there are several options. At about the same level, Perimeter Institute recorded a similar set of lectures. A somewhat longer set of lectures was given at EPFL, and these are fully written up and posted on Inspire. Finally there is a full semester long course with notes and videos.

**Lecture 1** Notes . Gravity as a field theory in parallel with the Standard Model. Why scalar exchange does not work. The role of the equivalence principle. The energy momentum tensor as a source. Currents as sources by gauging symmetries. Gauging time and space translation symmetries. The metric as a field. Writing an invariant Lagrangian. Success – E-M tensor as source. Preview of second success – Schroedinger equation in a gravitational potiential.

**Lecture 2** Notes Review. Covariant derivative. Curvatures from covariant derivatives. Invariant gravitational action. Einstein Equation. Weak field Limit. Gauge invariance. Harmonic gauge. The gravitational potential. Ghost stories – Feynman DeWitt ghosts, The ghost Lagrangian. Background Field Method. Higgs example. QED example.

**Lecture 3** Notes. Thinking like an effective field theorist. Rules for EFT. What are the quantum predictions? The general Lagrangian. Power counting. Results for scalar loop. EFT reasoning for potential – finite and parameter-free. What to expect. Calculation of potential. Pure gravity is one-loop finite. Graviton-Graviton scattering.

**Lecture 4** Notes Unitarity based methods. The double copy. Quantum bending of light. Classical physics from quantum loops, background field method for gravity, limits to the effective field theory.

**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.

Also I would like you to have access to Chapter 4 – Introduction to effective field theory from Dynamics of the Standard Model. This pdf version does not have the figures in place because Cambridge University Press added those. But I will draw the relevant figures during the lectures.

Feynman’s 1963 paper on the quantization of gravity . Fun to read!

I feel that all theorists interested in gravity should read Kibble’s classic paper which shows how gravity is constructed much like an standard gauge theory.

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.

A previous version of lectures on this topic – with considerable overlap – can be found using the notes for the TRISEP school, from Summer 2018. Perimeter has archived videos of those lectures.

Finally – the long version. I gave a semester-long course on this topic in 2015, and the notes are available here.

Although the topic will be only a small part of my lectures here, I thought I would post some of the papers describing interest in the **classical limit** of the effective field theory.

These include:

My favorite introduction to the method of regions is the lectures of Becher, written with Broggio and Ferroglia here.

Walter Goldberger’s lectures on the classical formalism that he and Rothstein pioneered.

Rothstein and collaborators has a paper on the classical limit.

My collaborators Emil and Pierre and their other collaborators also have a good paper on this topic.

And Kosower, Maybee and O’Connell have a detailed discussion of classical observables from quantum techniques.