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A Reading Guide to Loop Quantum Gravity (LQG):

This is a graduate-level guide to loop quantum gravity. I hope this will help the reader find the "pre-requisites" as well as some of the more contemporary work on this approach to quantum gravity. Suggestions are welcome.

You're encouraged not to read linearly (this is, after-all, a non-linear field!) For instance, you might start with the more recent book, "Quantum Gravity" by Carlo Rovelli, which covers most of these topics, or the older book of Abhay's ("Lectures..." - the little blue book), or the shorter, more inspirational, reviews and primers and then backtrack to pick up the background you find you need.

Be aware that the field has evolved greatly since the mid-1990's! I have retained older works, since they occasionally come in handy. I will (hopefully soon) include sections on the areas of spin foams and loop quantum cosmology.

Enjoy!

- Seth Major (based on an earlier reading list by Troy Schilling and myself)

Constrained Systems:

P.A.M. Dirac, Lectures on Quantum Mechanics, (Yeshiva, New York, 1964) [QC174.1.D55].
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, at least Chapters 1, 2, 4, and 13 (on quantization) (Princeton, 1992). [QC793.3.F5H46 1992].
Joe Romano, ``Geometrodynamics vs. Connection Dynamics'' in General Relativity and Gravitation, 25 (1993) 759 (This is Joe's Ph.D. thesis, Syracuse 1991).
Abhay Ashtekar, Lectures on Non-Perturbative Canonical Gravity, Appendix B, (World Scientific, Singapore, 1991) [QC178.A48 1991].

Hamiltonian Formulation of GR - 3+1:

R. Wald, General Relativity, Apendix E, (Chicago, 1984) [It's all in the book but you have to hop back and forth from chaper to appendix].
Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638.
A. Ashtekar, New Perspectves in Canonical Gravity , pg. 37, (Bibliopolis, Napoli, 1988) [QC178.A73 1988].

Connection Variables:

Abhay Ashtekar and Jerzy Lewandowski Background Independent Quantum Gravity: A Status Report gr-qc/0404018.
Carlo Rovelli, Quantum Gravity (Cambridge Univeristy Press, 2004) ISBN: 0521837332.
Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638.
Joe Romano, ``Geometrodynamics vs. Connection Dynamics'' in General Relativity and Gravitation, 25 (1993) 759 (This is Joe's Ph.D. thesis, Syracuse 1991).
A. Ashtekar, Mathematical problems of non-perturbative quantum general relativity in Les Houches 1992, [B. Julia ed., Les Houches 1992 (1994)].
Abhay Ashtekar, Lectures on Non-Perturbative Canonical Gravity, (World Scientific, Singapore, 1991) [QC178.A48 1991].

Quantization:

Abhay Ashtekar and Jerzy Lewandowski Background Independent Quantum Gravity: A Status Report gr-qc/0404018.
Thomas Thiemann, Lectures on Loop Quantum Gravity gr-qc/0210094.
Carlo Rovelli, Quantum Gravity (Cambridge Univeristy Press, 2004) ISBN: 0521837332.
Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638.
J. Pullin Knot Theory and Quantum Gravity in Loop Space: A Primer , hep-th/9301028 (breezy but still inspiring!).
Carlo Rovelli and Peush Upadhya Loop quantum gravity and quanta of space: a primer gr-qc/9806079 (updated but even more brief).
Rodolfo Gambini and Jorge Pullin Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge University Press 1996 ISBN 0-521-47332-2)
John Baez Gauge Fields, Knots and Gravity (World Scientific 1994 ISBN 981-02-2034-0 (paperback))[QC793.3.F5 B33 1994]
Volume 434 of Springer-Verlag's Lecture Notes in Physics, Canonical Gravity From Classical to Quantum is the proceedings of a conference held in September 1993.
R. Geroch, Geometrical Quantum Mechanics, pdf and a link to Rob Salgado's site with the LaTex source.
Abhay Ashtekar, Lectures on Non-Perturbative Canonical Gravity, Ch. 10, (World Scientific, Singapore, 1991) [QC178.A48 1991].

Classical Mechanics - Symplectic structures:

V.I. Arnold, Mathematical Methods of Classical Mechanics 2nd ed., pg. 201 (Springer-Verlag, New York, 1989) [QA805.A6813 1989].
A. Ashtekar, Lectures on Non-Perturbative Canonical Gravity, Appendix B, (World Scientific, Singapore, 1991) [QC178.A48 1991].

Fibre Bundles:

C. Nash and S. Sen, Topology and Geometry for Physicists , pg. 140, (Academic, London, 1983) [QA611.N35].
C. Isham, Modern Differential Geometry for Physicists, pg. 111 (World Scientific, 1989).
M. Nakahara, Geometry, Topology and Physics, Ch. 9, (Adam Hilger, 1990) [QA641.N35 1990].
A. Ashtekar, G. Horowitz, and A. Magnon-Ashtekar, General Relativity and Gravitation, 14 (1982) 411.
Y. Choquet-Bruhat and C DeWitt-Morette, Analysis, Manifolds and Physics, Amsterdam; N.Y., North-Holland Pub. (1981) [QC20.7.A5C48 1981].

Connections in Field Theory/on Principal Bundles:

Your favorite field theory book or L.D. Faddeev and A.A. Slavnov, Gauge Fields: Introduction to Quantum Theory, Ch 1 and 3 (an old style for field theory but closer to the language used around here) (Benjamin/Cummings, Reading, MA, 1980), [QC793.3.F5S5213].
L. Kauffman, Knots and Physics, pg. 293 (just after the little bit on SU(2)) (World Scientific, Singapore, 1991) [QC20.7.K56K38 1991] .
Jackiw in Les Houches, Relativity, B. DeWitt and R. Stora, eds. [QC174.13.R45 1984].
M. Nakahara, Geometry, Topology and Physics, Ch. 10, (Adam Hilger, 1990) [QA641.N35 1990].

Tetrads:

S. Weinberg, Gravitation and Cosmology, pg. 385 (Wiley, New York, 1972).
R. Wald, General Relativity, pg. 49, (Chicago, 1984).

Spinors:

W. Bede and H. Jehle, Rev. Mod. Phys. 25 (1953) 714 (old and from the point of view of the Dirac equation).
L. Kauffman, Knots and Physics, pg. 392 (esp. 398).
R. Penose and W. Rindler, Spinors and Spacetime Volume 1, (Cambridge, 1984) [QC20.7.S65P46 1984].
A. Trautmann, F. Pirani, and H. Bondi, Lectures on General Relativity, Ch. 3, (Prentice-Hall, 1965) [QC6.B675 1964].
G. Sterman, An Introduction to Quantum Field Theory, pg. 119, (Cambridge, 1993).
A. Ashtekar, Lectures on Non-Perturbative Canonical Gravity, Appendix A, (World Scientific, Singapore, 1991) [QC178.A48 1991].

Spin Networks:

Seth Major, ``A spin network primer'' Am. J. Phys. 67 (1999) 972-980 gr-qc/9905020.
Roberto De Pietri and Carl Rovelli ``Geometry eigenvalues and the scalar product from recoupling theory in loop quantum gravity'' Phys. Rev. D 54 (1996) 2664-2690.

Loops (for historical interest):

Jorge Pullin Knot Theory and Quantum Gravity in Loop Space: A Primer , hep-th/9301028 (breezy but inspiring!).
For a broad review try C. Rovelli in Living Reviews or Class. and Quantum Grav. 8 (1991) 1613 or L. Smolin in Proceedings of the XXII Gift International Seminar (World Scientific 1992). Or, read the orginal paper: C. Rovelli and L. Smolin. Nuc.Phys. B331 (1990) 80.
Carlo Rovelli Quantum Gravity (Cambridge University Press 2004) ISBN: 0521837332
B. Brügmann, On the constraints of quantum general relativity in the loop representation, Ph.D. thesis, Syracuse University (May 1993).
B. Brügmann, Loop Reprentations , gr-qc/9312001.
Thomas Thiemann, Modern Canonical Quantum Gravity (Cambridge Univeristy Press, 2007) ISBN 0521842638..
Abhay Ashtekar, Lectures on Non-Perturbative Canonical Gravity, Ch. 15 and 16, (World Scientific, Singapore, 1991) [QC178.A48 1991].
© S. Major 1993-2009 Last modified 10 June 2009 Link to Seth's Net Home Link to Department of Physics link to archives link to gr-qc link to gr-qc/new link to archive form