Class references

I am now keeping some of the class information on this page.

I will update a file containing many of the conventions of the course. Here is the present version.

Some sources for the GRQFT class
There is not a single book that matches the content of this course. Here are sources that I have found useful in constructing this course.

Steven Weinberg’s Gravitation and Cosmology book is one that many particle physicists like – and I am partial to it because I learned GR from it.

Some of the other GR books that have some field theory sensibility include Tony Zee’s GR in a Nutshell (some nutshell! It is huge. Perhaps a coconut shell.) which reads very well for self-study. Also T. Padmanabhan’s Gravitation is nice and I have found M. Gasperini’s Theory of Gravitational Interactions to be very useful.

There are books on QFT in curved spacetime. The original was by Birrell and Davies Quantum Fields in Curved Space. A more modern version is by Parker and Toms Quantum Field Theory in Curved Spacetime. Also there is an impressive book by Mukhanov and Winitzki. Introduction to Quantum Effects in Gravity. (Note that the draft for this book is available for free on Winitzki’s web page.) And of course there are the classics by Bryce DeWitt which contain so much good physics – The Global Approach to Quantum Field Theory and Dynamical Theory of Groups and Fields.

On the field theory side, my favorite resource is Dynamics of the Standard Model (2nd edition) by Donoghue, Golowich and Holstein. I will prepare some of the advanced QFT material using this. Matt Schwartz’s new QFT book Quantum Field Theory and the Standard Model is very good. Peshkin and Schroeder’s An Introduction to Quantum Field Theory is a classic.

Construction of GR as a gauge theory

This course starts with material that is basically from Weinberg’s Chapter 12.

The weak field limit and tree level Feynman rules

The weak field limit is covered in most GR books.

Advanced field theory techniques

Here are two appendices from Dynamics of the Standard Model that contains material related to the field theory techniques that I will be teaching:

Appendix A – Functional Integration

Appendix B – Advanced field theory methods

Also Gasser and Leutwyler chiral perturbation theory. This classic paper uses the background field method and the heat kernel similar to the way we will treat general relativity.

Vasselivich – Heat Kernel Expansion – a user’s manual

Quantization of GR

For the quantization of GR section, the classic paper is that of
‘t Hoof and Veltman. It takes a bit to get used to their conventions (i.e. they use the (x,y,z,ict) convention)
but they are the definitive treatment of the quantization procedure. The paper is here.

Also useful is Veltman’s Les Houches lectures from the same period:
Veltman Quantum_theory_of_gravitation

Feynman’s Acta Physica Polonica article Quantum Theory of Gravitation is very entertaining and enlightening to read.

Effective field theory of GR

I have put together a whole page of references on this topic.

Weinberg’s paper on Infrared photons and gravitons is an important early paper.

Fermions, torsion and all that

Kibble on fermions and gauge structure

Shapiro – Physics Reports on torsion

Hayashi Shirafuji – a remarkably good early paper in the spirit of effective field theory (although I would do some things differently).

Hehl et al. GR with spin and torsion review


Ch. 3 Symmetries and Anomalies from Dynamics of the Standard Model

There is much material on gravitational anomalies in the books by Birrell and Davies and by Parker and Toms.

Hawking radiation

Here are some of the papers that I have found useful.

The book by Mukhanov and Winitski was useful in preparing the lectures. I can’t post the book but here are the chapters on Unruh and Hawking from Wintitski’s online draft version.

Collected references and lectures