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September, 1994
Reading Guide to the New Variables
Our intention in creating this list is to compile a guide to the
new variables. We hope this will help you to find the ``prerequisites'' as
well as some of the more contemporary work on this approach to
quantum gravity.
We've divided the list into ten fields.
In each field we've listed references roughly in order of
difficulty/sophistication.
You're encouraged not to read linearly
(this is, afterall, a
nonlinear field!)
For instance, you might start with the more
recent book by Abhay known as ``Lectures...'' (the blue book), the older
``New Perspectives...'' or the shorter, more inspirational,
``Primer'' by Jorge and then backtrack to pick
up the background you find you need.
For information not covered here, ask around!
Let us know about your favorite references.
 Seth Major and Troy Schilling
Since we completed this list, two books have been brought to our attention:
John Baez has a new introductory book!
Gauge Fields, Knots and Gravity
(World Scientific 1994 ISBN 9810220340 (paperback))
Volume 434 of SpringerVerlag's Lecture Notes
in Physics , Canonical Gravity From Classical to Quantum is
the proceedings of a conference held in September 1993.
Classical Mechanics  Symplectic structures:
 Joe Romano's notes or Geroch's notes,
Geometrical Quantum Mechanics
[unpublished Chicago lecture notes  there is a copy in the preprint
lounge].
 V.I. Arnold, Mathematical
Methods of Classical Mechanics 2nd ed., pg. 201 (SpringerVerlag,
New York, 1989)
[MATH QA805.A6813 1989].
 A. Ashtekar, Lectures on NonPerturbative Canonical
Gravity, Appendix B, (World Scientific, Singapore, 1991) [QC178.A48 1991].
Constrained Systems:
 P.A.M. Dirac,
Lectures on Quantum Mechanics,
(Yeshiva, New York, 1964) [Annex QC174.1.D55].
 M. Henneaux and
C. Teitelboim, Quantization of Gauge Systems, Chs. 1, 2 and 4,
(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).
 A. Ashtekar, Lectures on NonPerturbative 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].
 A. Ashtekar, New Perspectves in Canonical Gravity , pg. 37,
(Bibliopolis, Napoli, 1988) [QC178.A73 1988].
New Variables:
 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 nonperturbative
quantum general relativity in Les Houches 1992, [B. Julia ed., Les
Houches 1992 (1994)].
 A. Ashtekar, Lectures on NonPerturbative Canonical
Gravity, (World Scientific, Singapore, 1991) [QC178.A48 1991].
Loop Representation:
 J. Pullin Knot Theory and Quantum Gravity in Loop
Space: A Primer , hepth/9301028 (breezy but inspiring!).
 For a broad review try C. Rovelli. 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.
 B. Brügmann, On the constraints of quantum general relativity
in the loop representation, Ph.D. thesis, Syracuse University (May 1993).
 B. Brügmann, Loop Reprentations , grqc/9312001.
 A. Ashtekar, Lectures on NonPerturbative Canonical
Gravity, Ch. 15 and 16, (World Scientific, Singapore, 1991) [QC178.A48 1991].
Quantization:
 R. Geroch, Geometrical Quantum Mechanics, unpublished lecture
notes, Univ. of Chicago.
 A. Ashtekar, Lectures on NonPerturbative Canonical
Gravity, Ch. 10, (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. MagnonAshtekar,
General Relativity and Gravitation, 14 (1982) 411.
 Y. ChoquetBruhat and C DeWittMorette,
Analysis, Manifolds and Physics, Amsterdam; N.Y., NorthHolland 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) [Math QC20.7.S65P46 1984].
 A. Trautmann, F. Pirani, and H. Bondi, Lectures on
General Relativity, Ch. 3, (PrenticeHall, 1965) [Annex QC6.B675 1964].
 G. Sterman, An Introduction
to Quantum Field Theory, pg. 119, (Cambridge, 1993).
 A. Ashtekar, Lectures on NonPerturbative Canonical
Gravity, Appendix A, (World Scientific, Singapore, 1991) [QC178.A48 1991].
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Jorge Pullin
Tue Jan 9 16:22:08 EST 1996