In the Spring semester of 2015, I taught a course (P852) on an introduction to General Relativity as a Quantum Field Theory. The primary intent was to describe General Relativity as a quantum field theory, in parallel with our other fundamental interactions. It is constructed in a manner similar to gauge theories, and is quantized and field theory calculations are performed. This is quite different from the usual approach as a geometric theory.
This was aimed at students who have had one semester of QFT, so it also functioned as a Quantum Field Theory II course. The overall content of the course had the form:
Constructing GR through gauge invariance
The weak field limit of GR and tree level Feynman rules
Some field theory techniques:
– Heat kernel methods
– Background field method
– Gauge fixing and ghosts
Path integral quantization of General Relativity
Effective field theory
General relativity as an effective field theory
Fermions, torsion, Holst and all that
Anomalies in gauge theory
Unruh and Hawking radiation
In this listing the items in italics are straight QFT II topics, and the rest refer to the quantum field theory of General Relativity.
A more detailed outline gives the day-by-day content.
The notes for this course have been collected and the course itself has been recorded. The recordings are relatively primitive, and we had some technical glitches. But this is what it is, and these are presented in case they are useful for anyone in the future.
The lecture material is here. References for the course are also found on that page.