Quantum Gravity Resources

Derek K. Wise

This page is designed to be a gateway to some resources on quantum gravity and related topics. The usual sort of website disclaimers apply, e.g. omissions obviously don't imply anything about my opinion. I'm not making any attempt to be comprehensive, representative, or unbiased. These are just some resources I find helpful or interesting, mainly resources freely available online, though I'll also cite some books. I'm just beginning to build this page (Jan 2008), and I hope to expand it in the coming months.

One reason for starting this page is that I'm organizing a seminar this quarter in the Math Department at U.C. Davis. This seminar had been the "string theory seminar", but this quarter is titled "Quantum Gravity and Strings", since (1) I'm not a string theorist, and (2) the seminar in fact has a broader focus than just string theory. I will post resources here that may be interesting to the seminar's members, including links relevant to upcoming talks.

I've just started adding links to the sections below. More links will appear soon....

Broad Overviews of Quantum Gravity

Here are some articles that try to give an overview of the main problems of quantum gravity, and survey various approaches to the subject. While parts of these reviews are somewhat out of date, I think they are all still quite helpful.

Chris Isham, "Structural issues in quantum gravity". (gr-qc/9510063) [This is the oldest review listed here, but still one of my favorites. An excellent relatively nontechnical introduction to conceptual problems of quantum gravity.]
Jeremy Butterfield and Chris Isham, "Spacetime and the Philosophical Challenge of Quantum Gravity". (gr-qc/9903072)
Gary Horowitz, Quantum gravity at the turn of the millennium. (gr-qc/0011089)
Claus Kiefer, "Quantum gravity: general introduction and recent developments", (gr-qc/0508120)
Steve Carlip, Quantum gravity: a progress report". (gr-qc/0108040)

Also interesting is the "historical" appendix of Rovelli's book on loop quantum gravity, listed below. Roger Penrose's recent book, The Road to Reality includes good introductory reviews of various approches

The excellent website Einstein Online also has a special section on Relativity and the Quantum

Foundational Issues

The problem of time

Lee Smolin is teaching a class right now on the problem of time: Fortunately for those of us who aren't at PI, the videos will appear online:

Lee Smolin, The Problem of Time in Quantum Gravity and Cosmology

Lecture 1 (9 Jan 2008). Introduction to the course, and general introduction to the problem of time, including some of the history and philosophical stances. This first lecture is a fairly nontechnical overview. One of Lee's main points seems to be that in truly fundamental theories the only notion of "clock" should be part of the system being studied. (Advance your viewer to ... uh... "time" 1:20:40 to see a preview of the rest of the course, including the detailed syllabus.)
Lecture 2A (16 Jan 2008) Hamiltonian general relativity (and why it is needed for understanding the problem of time); Dirac's approach to constrained Hamiltonian systems.
Lecture 2B

Loop Quantum Gravity and Spin Foams

Videos of Lee Smolin's Introduction to Quantum Gravity at PI.
(Parts 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19^*, 20^*, 21^*, 22^†, 23^†, 24, 25)

^†

Carlo Rovelli's LQG article at Living Reviews in Relativity. A more complete reference is Rovelli's book Loop Quantum Gravity (Cambridge Monographs on Mathematical Physics). An early version is available in pdf. (One good reason to actually purchase the book, besides the nice format and various improvements and corrections, is that the pdf version lacks the index).

Thomas Thiemann, Modern Canonical Quantum General Relativity (Cambridge Monographs on Mathematical Physics). An early version is available as gr-qc/0110034

John Baez, An introduction to Spin Foam Models of BF theory and quantum gravity, gr-qc/9905087.

String Theory

An introduction targeted at people like me:

Donald Marolf, "String/M-branes for relativists". (gr-qc/9908045)

Also see Marolf's nice bibliography of introductory and review literature on strings.

String theory attempts to be much more than just a theory of quantum gravity, but if you are mainly interested in how strings provide a theory of quantum gravity, the following book might be helpful (So far, I haven't gotten ahold of a copy myself, but it looks like it should be very interesting):

Tomás Ortín, Gravity and Strings, (Cambridge Monographs on Mathematical Physics)

Causal Sets

Geometry from order: causal sets (an article at the website "Einstein Online", mentioned above)

David Reid, "Introduction to causal sets" (gr-qc/9909075).

Causal Dynamical Triangulations

The first place I learned about CDTs was probably when I went to Renate Loll's talk at Loops '05. One of the most interesting points in her talk is that CDTs modeling 4d spacetime actually appear 2-dimensional at short distances, suggesting a connection with the spin foam approach to quantum gravity. Unfortunately, it is hard to see the slides in this video, and there are some audio problems after some point, but I think one can still get a good idea of what the approach is about by listening to the audio. You can also read this paper by Loll and her collaborators:

J. Ambjorn, J. Jurkiewicz, and R. Loll, "Reconstructing the universe". (hep-th/0505154)

Other approaches

NCG, TQFTs and generalizations, twistor theory, ...

"Background Material"

It is hard to know what "background material" is necessary for understanding quantum gravity, since we don't yet know what quantum gravity is. In my view, it is very likely that the prerequisites -- on both physical and mathematical levels -- are still too poorly understood. But, to do any sensible work on the subject, one must clearly know the two theories quantum gravity seeks to supplant: classical general relativity and quantum field theory. Whether or not you believe gravity can only be quantized as part of a broader unification scheme that includes the other fundamental forces (a matter of serious contention!) it is also good to know the standard model of particle physics, based on quantum field theory.

It's much harder to know what mathematical prerequisites are needed for studying quantum gravity, aside from the mathematics underlying gravity and quantum field theory.

Here I'll list some of my own favorite resources on these subjects (besides the standard textbooks):