If you thinking that studying Quantum Gravity will make you a happy person, despite having read this, you find below some answers to questions frequently asked by students. Please feel free to write me if you need more informations or if you have a question that you think it would be usefull to find answered here. This page is still under construction: I plan to post here more informations about studying Quantum Gravity (references, institutions, schools, advises...).
There is a rich literature on loop quantum gravity. On quantum gravity in general, Claus Kiefer has a recent general introduction. Many approaches are also reviewed in the collection edited by Daniele Oriti. Asktekar and Petkov are editing a "Springer Handbook of Spacetime", which will contain numerous useful contributions.
A nice book with much useful background material is John Baez and Javier Munian's. Baez has also another older book, with many ideas and a nice introduction to the subject. An undergraduate level introduction to loop quantum gravity is provided by the book by Rodolfo Gambini and Jorge Pullin, which contains various entry level material. Gambini and Pullin have also written an older text, which describes an earlier stage of the understanding of the theory and emphasizes the relation with gauge theories. The very early form of the theory and the first ideas giving rise to it can be found in the 1991 book by Abhay Ashtekar. A detailed text on the canonical formulation of the theory, rich in mathematical details, is the text by Thomas Thiemann. Martin Bojowald has recently published a text with introductory material in canonical gravity and focused on quantum cosmology.
A good recent reference is the collection of the proceedings of the 3rd Zakopane school on loop quantum gravity, organized by Jerzy Lewandowski. In contains in particular an introduction to loop quantum gravity by Abhay Ashtekar, Carlo Rovelli's "Zakopane lectures", the introduction by Kristina Giesel and Hanno Sahlmann to the canonical theory, and John Barrett et al review on the semiclassical approximation to the spinfoam dynamics.
Last but not least, Carlo Rovelli and I are writing a new introductory text. A preliminary draft is here: suggestions are welcomed!
Hamiltonian Mechanics and constrained systems, Quantum Mechanics and in particular representation theory and recoupling theory, General Relativity and in particular its tetrad formulation, Quantum Field Theory and in particular non-abelian field theories, gauge theories on a lattice, renormalization theory. Plus many other things... Quantum Gravity is a theory in fieri, where problems may need new technics to be solved: maybe some experience of yours, that now seems unrelated, may turn out to play a key role to solve a problem in the future. Be open to learn!
Supposing you already know QM and GR, my suggestion would be to read Baez's book "Gauge Fields, Knots, and Gravity" (very good to learn the tetrad formalism and the ADM formalism for GR, that are prerequisits to understand LQG), then the new book by Gambini and Pullin A First Course in Loop Quantum Gravity. You can also take a look to the Introductory lectures to loop quantum gravity (it is actually the master thesis of Pietro Doná) that is available online for free.
If you have also already studied QFT, you can start to read about the covariant (path integral) formalism in LQG, called Spinfoam Theory. There is a huge literature in LQG, but mostly this is not too much concerned about Spinfoam. For this, there is a recent Living Review in Relativity by Alejandro Perez, and our new book, of course! You can also find a full crash class by Carlo Rovelli, that is completely available online at the Pirsa.
There is a google map, where you find listed all the institutions where you can study quantum gravity. Not all these institutions host a proper LQG group, but an institution is listed if there is a permanent member of the stuff that can supervise a stage or a thesis in LQG.
That's a tricky question. Every place has some plus and some minus. And what makes actually a place to be good, is the student's attitude: so it would depend if there is a specific subject that interest you, and also on a bit of alchemy with the other members of the group. Some important groups can be very crowded: this means that you have the great opportunity to talk with a lot of people, but it also require you to be able to work independently. In smaller groups, you may find less external stimula, but you may also find a dedicated advisor that can be of fundamental help to make the first moves in the subject.
You need to have taken at least a class on quantum mechanics and an introductory class to general relativity. Then, the more you have studied quantum field theory, the better, but you can do a project even without. You should not expect to solve the final theory of quantum gravity, but sometimes studing a small project on some basic issue of the theory can take you to interesting and relevant new insights, possibly leading to a publication.
If you are looking for a stage, take a look here.
First of all, scan the websites such as hyperspace.
Then, target the professors working on the subject of your interest, write them explaining your research interests, and propose yourself for a visit and a blackboard presentation of your master project. While asking for PhD fellowships, keep in mind that sometime foundings can become available in different time, that sometimes professors have to apply for fundings having already the name of a candindate, and that networking is always good: so get in touch with people doing things you like, even if there is not a specific call for PhD.
The field of Quantum Gravity does not have huge foundings, so there are only a few dedicated scolarships. Most of the people who have studied quantum gravity so far, they secured their own schoolarship by applying for instance to national calls or internationals calls. Note that, according of the laws in many countries, France for instance, you cannot enroll in a PhD if you have not a scholarship for the full duration of your studies (you cannot just say that you pay yourself for your living).
Good notes may make a good first impression, but what would really make you succed would be: showing to know the kind of research that is done in the group and your genuine interest for it (even if you don't have previous competence), proposing yourself for a visit of the group and giving a short presentation (it could be your bachelor or master project: better to do it even if you worked on a different subject, better at the blackboard but carefull: using the blackborad is an art! if you don't feel confident, better to prepare some slides).
The main question while evaluativìng a candidate is: how many chances has him/her to become a leader scientist or thinker? Technical skills are valued, but also, if not more, independence, creativity, understanding, and being reasonable.
This may vary a lot from place to place.
In Europe a PhD last usually 3 years. You will have to attend some classes (much less involving then your previous classes) and you may have the possibility to teach.