In the Fall of 2015, I was the Erwin Schrödinger visiting professor at the University of Vienna, and gave a series of lectures. The notes for this and some supplementary material are given on this page.
References for the lectures will be linked here:
Construction of GR as a gauge theory
A great early reference along the lines that I presented the material is Kibble on fermions and gauge structure
The other primary reference is Utiyama on Gravity as a gauge theory.
I have an appreciation of a paper by
Hayashi and Shirafuji – a remarkably good early paper in the spirit of effective field theory (although I would do some things differently).
Weinberg’s GR textbook has a related development, but without fermions, in Chapter 12.
I highly recommend Maurizio Gasperini’s book Theory of Gravitational Interactions (Springer) as a resource if you are interested in following up on this material. Even though he does not construct GR in this fashion, his treatment is more general than most and he derives many useful relations.
An overview with more on the possibility if torsion is Hehl et al. GR with spin and torsion review
Effective field theory of GR
Here is Feynman’s 1963 “Quantum theory of gravitation”. It is fun to read, and historically very important.
‘t Hooft and Veltman’s paper on the quantization and renormalization of gravity is a classic.
Appendix B from Dynamics of the Standard Model has an explanation of the heat kernel method, although it is is flat space.
Andrei Barvinsky has a Scholarpedia article on the heat kernel in gravity.
I have put together a whole page of references on the effective field theory treatment.
Weinberg’s paper on Infrared photons and gravitons is an important early paper.
Low energy theorems of quantum gravity
Here I just give links to some papers relevant for the topics discussed in this lecture:
My paper with Holstein on classical physics from quantum loops.
The calculations of the Reissner-Nordstrom metric that I used as an example.
The calculation of the gravitational potential
One of the papers by Zvi Bern on gravity as the square of gauge theory.
An explicitly worked out example of the double copy relation, by Holstein.
A great introduction to modern techniques in scattering amplitudes by Elvang and Huang. They also have an expanded version as a book.
The calculation of the gravitational potential without loops, along with the universality argument.
Light bending and equivalence principle violation.
Graviton-graviton scattering by Dunbar and Norridge, and the
infrared resolution.
Non-local effective action and hints of singularity avoidance.
Finally, a talk of mine entitled “When effective theories fail”.