[Paper Review] EPFL Lectures on General Relativity as a Quantum Field Theory

John F. Donoghue, Mikhail M. Ivanov+1 more|arXiv (Cornell University)|Feb 1, 2017

Black Holes and Theoretical Physics64 references64 citations

TL;DR

These notes recast General Relativity as a quantum effective field theory, outlining a gauge-theory construction of GR, its quantization, and EFT properties, with developments in weak-field gravity, background-field methods, and infrared aspects.

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.

Motivation & Objective

• Motivate building gravity from quantum field theory using EFT concepts.
• Construct GR by gauging spacetime translations and identify the energy-momentum tensor as the source.
• Develop the GR action and dynamics from a gauge-theoretic viewpoint with matter coupling.
• Present techniques like the background-field method, heat kernel, and EFT framework for gravity.
• Outline IR properties, non-local EFT actions, and conceptual developments in quantum gravity.

Proposed method

• Present the gravity field g_{μν} as the dynamical field sourced by the energy-momentum tensor T_{μν}.
• Gauges the translation symmetry to obtain a gravitational field and derives the Einstein-Hilbert action as the gravity sector.
• Introduce vierbeins e^{a}_{μ} to connect Lorentz and world indices and formulate fermions in curved spacetime.
• Develop the weak-field expansion g_{μν}=η_{μν}+κ h_{μν} and derive propagators and Feynman rules.
• Apply the background-field method and discuss gauge fixing, Faddeev–Popov ghosts, and their role in GR.
• Use heat-kernel techniques to study quantum corrections and discuss the Gauss–Bonnet term and holographic-like structures.
• Explain the principles of effective field theory and how GR fits into a general EFT framework.
• Explore one-loop corrections to Newton’s potential and the generation of metric structures (e.g., Reissner–Nordström) via loops.
• Discuss gravity as a square of gauge theory and nonlocal effective actions as frontier topics.
• Investigate infrared properties, soft theorems, and the role of BMS transformations in gravity.

Experimental results

Research questions

• RQ1 How can General Relativity be formulated and understood as a quantum effective field theory?
• RQ2 What is the role of the energy-momentum tensor as the source of gravity in a gauge-theoretic construction?
• RQ3 How do background-field methods, Feynman rules, and heat-kernel techniques apply to gravity quantization within EFT?
• RQ4 What are the infrared properties and soft theorems of quantum gravity, and how do they relate to GR?
• RQ5 What insights arise from viewing gravity as a square of gauge theory and from nonlocal EFT actions?

Key findings

• GR can be formulated as a quantum effective field theory with a well-defined EFT framework.
• The energy-momentum tensor acts as the source for the gravitational field in a gauge-theory construction of GR.
• Weak-field GR can be treated with propagators and Feynman rules, enabling loop corrections such as the one-loop Newton potential.
• The Einstein–Hilbert action and matter couplings arise from gauging spacetime translations and introducing vierbeins and connections.
• Background-field methods and ghosts generalize to GR, enabling systematic quantum corrections within EFT.
• IR divergences in GR exhibit cancellations and are connected to soft theorems such as Weinberg’s and BMS transformations.