EPFL Lectures on GR as a QFT

At the EPFL Lausanne, I gave a series of lectures totaling about 14 hours in October 2016. This provides a more detailed look at many topics, but is not so extensive as the full semester course that I offered at UMass in 2015. It has the advantage that it has been typed up by two of the students in the class – thanks to Andrey Shkerin and Mikhail Ivanov. This is available on the web at inSpire.

I gave a short course on General Relativity as a Quantum Effective Field Theory (link here) at the EPFL in Lausanne, Sept 22 – Oct 13, 2016, as part of the Conference Universitaire de Suisse Occidentale doctoral program. This page has the notes and references of that short course. Other pages on this website contain a longer course which I gave at UMass, as well as more references. This website is not meant as a complete treatment of this subject, but I hope to keep improving the pages.

Typed notes Andrey Shkerin and Mikhail Ivanov have worked hard to type up the notes for the lectures. The structure and most of the formulas are basically as given in the lecture and the words are their paraphrase of what I said. Thanks for doing this!

The combined typed lectures, and an extension written by Andrey and Mikhail is now available here and on the arXiv.

1) Constructing general relativity as a field theory

Class notes: First lecture Part 1 on general relativity as a gauge theory, Part 2 on fermions and the spin connection and Part 3 on the weak field expansion and simple solutions.

Andrey and Mikhail’s typed notes fir the first class are found here.

Some classic references:



In response to a class question about the general coupling of scalars:

Damour Donoghue paper on general dilaton couplings

2) Content and quantization

Class notes: Second lecture Part 1 on gravitons and Feynman rules, Part 2 on the background field method, gauge fixing and ghosts, and Part 3 on heat kernel methods and loops.

Andrey and Mikhail’s typed notes are here.

Some references for this lecture:

Feynman – the earliest quantization

‘t Hooft and Veltman

Abbott Background Field Method

Appendix B from Dynamics of the Standard Model with heat kernel discussion

Heat kernel and background field for gravity – Barvinsky

3) Effective field theory

Lecture note for third week. Why do quantum calculations work?, first principle – locality vs non-locality, second principle – the energy expansion, third principle – loops renormalization and matching/measuring, constructing an EFT explicitly with the linear sigma model, example of a scattering amplitude, Haag’s theorem, integrating out a heavy field, higher order matching at tree level, renormalization of the EFT, matching at one loop, power counting and Weinberg’s theorem, low energy QCD as an EFT, background field construction, measuring and predictions.

Andrey and Mikhail’s notes are here.

Here are some references:

Chapter 4 of Dynamics of the Standard Mode – Introduction to Effective Field Theory

Chapter 7 of Dynamics of the Standard Model – The Effective Field Theory of Low Energy QCD

4) General relativity as an effective field theory

On the fourth day of the course, part 1 was on the construction and renormalization of GR as an effective field theory. Part 2 covers the techniques for making predictions in an effective field theory, as well as the topics of GR as the square of a gauge theory and unitarity techniques. The third segment was a tour of anomalies in general, gravitational anomalies as an IR effect, and non-local effective lagrangians.

Andrey and Mikhail’s typed notes for the core part of Lecture 4 can be found here.

Andrey and Mikhail have also produced a supplement that went beyond the lectures in discussing the soft limits of the theory. This contribution is of their own design. Their notes are here.

Finally I wrote up a guide to the third segment of this lecture on anomalies and no-local actions. It is posted here.

References for this lecture:

My original paper on GR as an EFT

Our paper on the Reissner-Nordstrom metric has some pedagogic value.

Bern review on gravity as the square of a gauge theory

Weinberg Infrared photons and gravitons

Chapter 3: Symmetries and Anomalies from Dynamics of the Standard Model.

The papers with my former student Basem El-Menoufi on trace anomaly, on the non-local curvature expansion
and on log corrections in gravity are somewhat gentle introductions to non-local effective actions. There are references in these papers to the original Barvinsky – Vilkovisky papers which pioneered these techniques, although these papers are not as gentle.

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

Scholarpedia entry

Collected references and lectures