4 Resources
The best way to learn a theory is to read different presentations of the same theory and appreciate
different points of views. This is particularly true for a theory, which is tentative and in evolution, like
loop quantum gravity. Here is a list of textbooks and introductions to the theory, and other
resources.
- Textbooks:
- Rovelli’s book [261
] is a general introduction to loop quantum gravity. It contains a first
part in which the main conceptual problems of quantum gravity are discussed, and both
general relativity and quantum mechanics are reformulated in a form suitable for their
merge. The second part is a detailed introduction to the formalism, with the derivation
of all basic results. The emphasis is more on the physical ideas and intuition than on
mathematical completeness.
- Thiemann’s book [294] is more mathematically oriented and a bit harder to read. It
is far more complete than my book, particularly on the definition of the Hamiltonian
operator, matter, etc. Apart from some occasional divergence, the two books can be read
as a two-part (“I: Conceptual basis and physical introduction” and “II: Mathematical
formalism”) text on loop quantum gravity.
- Ashtekar’s old book [18] may serve as a valuable basic introductory course on Ashtekar
variables, particularly for relativists and mathematicians. (The part of the book on the
loop representation is essentially a reprint of the original article [265]. For this quantum
part, I recommend looking at the article, rather than the book, since the article is more
complete.)
- The book by Gambini and Pullin [128] is especially good on lattice techniques and on the
variant of loop quantum gravity called the “extended loop representation” [100, 99].
- An interesting collection of papers can be found in the volume [46] edited by John Baez.
The other book by Baez and Muniain [55] is a simple and pleasant introduction to several
ideas and techniques in the field.
- Introductions:
- This “living review” may serve as a simple introduction to some basic ideas of quantum
gravity in the loop formalism.
- Ashtekar and Lewandowski [33] have a good introduction to loop quantum gravity that
balances mathematical precision with physical ideas.
- Smolin’s “Invitation to loop quantum gravity” [277] is readable and complete, especially
for possible physical consequences of the theory.
- Thiemann’s lectures [292] (not to be confused with the book) are a very good and readable
straightforward introduction to loop quantum gravity.
- Ashtekar has another nice introduction, especially to the recent advances in the field
(“Four recent advances and a dozen frequently asked questions”), in [21].
- Perez’s lectures [230] give a very nice pedagogical introduction to loop gravity, including
the spin-foam formalism.
- PhD Theses. Of the numerous very good PhD theses that are online, I single out the one
of Daniele Oriti [213], with a nice introduction to the spin-foam formalism.
- An old, but interesting, general introduction to the new variables, which includes several
of the mathematical developments in the quantum theory, is given by Ashtekar’s Les
Houches 1992 lectures [19]. Another simple introduction is in [241].
- Others:
- Several good listings of introductory literature to the subject can be found on the web.
See for instance:
- The “Basic curriculum for Quantum Gravity” in the “Christine’s Background
Independence” page of Christine C. Dantas [95] (scroll down).
- The “Reading Guide to loop Quantum Gravity” by Seth Major [189].
- Dan Christensen’s webpage [87].
- The webpage of the Loop Quantum Gravity Group of the National University of
Singapore [208].
- A resource for finding relevant literature is the comprehensive “Bibliography of Publications
Related to Classical and Quantum Gravity in terms of Connection and Loop Variables”,
organized chronologically. The original version was compiled by Peter Hübner in 1989. It has
subsequently been updated by Gabriella Gonzales, Bernd Brügmann, Monica Pierri, Troy
Shiling and Christopher Beetle. It is now updated by Alejandro Corichi and Alberto Hauser. The
latest version can be found on the net at [91].
- Lee Smolin’s “Introduction to Quantum Gravity” course is online [272].
- And so are the notes of John Baez’s “Quantum gravity seminar” [40].
- The loop gravity community (often extended to several other non-string approaches) meets at regular
conferences. The last meetings have been LOOPS 04 in Marseille, France [185], LOOPS 05 in
Potsdam, Germany [186], and LOOPS 07 in Morelia, Mexico [187].
- Some of the institutions where loop quantum gravity is studied are
- Institute for Gravity and Geometry [222], Penn State University, PA, U.S.A.
- Perimeter Institute [232], Waterloo, ON, Canada.
- Albert Einstein Institute [200], Potsdam, Germany.
- Louisiana State University, Baton Rouge, LA, U.S.A.
- Center of Theoretical Physics of Luminy [172], Marseille, France.
- The University of Nottingham, Nottingham, U.K.
- Warsaw University, Warsaw, Poland.
- CSIC, Madrid, Spain.
- UNAM, Mexico City, Mexico.
- Ecole National Superieur, Lyon, France.
- Scuola Nazionale Superiore di Pisa, Pisa, Italy.
- Beijing Normal University, Beijing, China.
- Université de Tours, Tours, France.
- Université de Montpellier, Montpellier, France.
- Universitá di Bologna, Bologna, Italy.
- Morelia University, Morelia, Mexico.
- Imperial College [153], London, U.K.
- Institute for Theoretical Physics, Utrecht, The Netherlands.
- Universidad de la República, Montevideo, Uruguay.
- University of Western Ontario, London, ON, Canada.
- University of New Brunswick, Saint John, NB, Canada.
- University of Massachusetts at Dartmouth, Dartmouth, MA, U.S.A.
- Hamilton College, Clinton, NY, U.S.A.
