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EPFL Lectures on General Relativity as a Quantum Field Theory

John F. Donoghue, Mikhail M. Ivanov, Andrey Shkerin

TL;DR

The notes recast General Relativity as a quantum effective field theory, built from a gauge‑theoretic viewpoint by gauging translations and treating the energy–momentum tensor as the gravity source. They develop technical tools—weak‑field quantization, the background field method, and the heat‑kernel approach—to obtain tree‑level and one‑loop predictions, including Newtonian corrections and nonlocal effects, while emphasizing EFT principles such as locality, derivative expansion, and matching. The text also explores infrared structures, soft theorems, and the connection Between GR and YM theories via the double copy, and it culminates in nonlocal effective actions and the broader outlook on quantum gravity within the EFT framework. Overall, gravity is shown to be a well‑defined, predictive EFT at accessible energies, with a clear path toward deeper UV completions.

Abstract

These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field theoretic viewpoint, and to introduce some of the techniques needed to understand the subject.

EPFL Lectures on General Relativity as a Quantum Field Theory

TL;DR

The notes recast General Relativity as a quantum effective field theory, built from a gauge‑theoretic viewpoint by gauging translations and treating the energy–momentum tensor as the gravity source. They develop technical tools—weak‑field quantization, the background field method, and the heat‑kernel approach—to obtain tree‑level and one‑loop predictions, including Newtonian corrections and nonlocal effects, while emphasizing EFT principles such as locality, derivative expansion, and matching. The text also explores infrared structures, soft theorems, and the connection Between GR and YM theories via the double copy, and it culminates in nonlocal effective actions and the broader outlook on quantum gravity within the EFT framework. Overall, gravity is shown to be a well‑defined, predictive EFT at accessible energies, with a clear path toward deeper UV completions.

Abstract

These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field theoretic viewpoint, and to introduce some of the techniques needed to understand the subject.

Paper Structure

This paper contains 64 sections, 395 equations, 2 figures, 1 table.

Table of Contents

  1. Constructing GR as a Gauge Theory: A QFT Point of View
  2. Preliminaries
  3. Gauge Theories: Short Reminder
  4. Abelian Case
  5. Non--Abelian Case
  6. Gravitational Field from Gauging Translations
  7. General Coordinate Transformations
  8. Matter Sector
  9. Gravity Sector
  10. Fermions in General Relativity
  11. Weak--Field Gravity
  12. Gauge Transformations
  13. Newton's Law
  14. Gauge Invariance for a Scalar Field
  15. Schr$\ddot{\text{o}}$dinger equation
  16. ...and 49 more sections

Figures (2)

  • Figure 1: One--loop diagram providing quantum corrections to the Coulomb or Newton's potential. Dotted line represents the cut.
  • Figure 2: One--loop diagram providing quantum corrections to the light bending. The dashed lines represent massless field (scalar or photon), the solid line --- the massive field, and the dotted line represents the cut.