Loop Quantum Gravity Literature
Ignacy Sawicki
started a literature search, but know very little of the subject so far.
I'd be very grateful for any pointers to recent(ish) reviews of the
subject, and any books that I might find useful. I have the Rovelli "Living
Reviews" review, I've found a short primer by Rovelli and Upadhya on ArXiv,
and a couple of Rovelli articles on the approaches to quantum gravity in
general. But that's it, as far as reviews are concerned -- nothing since
1998! I'm not even sure how relevant the Rovelli "Living Reviews" article
is, considering the state of knowledge in the subject five years later.
I would also appreciate any pointers to good textbooks dealing with the
physics that is assumed in the subject. To give you an idea of my level, I
have graduate-level QFT, I've done 3+1 decompositions of GR and the
Wheeler-de Witt equation, but I've not heard of spin connections or Wilson
loops before, for example.
Thanks for your help,
Iggy
John Baez
Ignacy Sawicki <sp...@barrier.com> wrote:
>I wish to study Loop Quantum Gravity for my Masters dissertation. I have
>started a literature search, but know very little of the subject so far.
>
>I'd be very grateful for any pointers to recent(ish) reviews of the
>subject, and any books that I might find useful. I have the Rovelli "Living
>Reviews" review, I've found a short primer by Rovelli and Upadhya on ArXiv,
>and a couple of Rovelli articles on the approaches to quantum gravity in
>general. But that's it, as far as reviews are concerned -- nothing since
>1998! I'm not even sure how relevant the Rovelli "Living Reviews" article
>is, considering the state of knowledge in the subject five years later.
It's EXTREMELY relevant! We've made progress since then, but
the stuff known then is still known, and still very important.
So, if you're just getting started on loop quantum gravity, you should
carefully study Carlo Rovelli's article:
http://relativity.livingreviews.org/Articles/lrr-1998-1/
before moving on to more detailed stuff. Rovelli is updating this
website now, and also writing a textbook on loop quantum gravity,
but for now this is *the* place to start learning the subject.
When you want more detail, try this:
http://www.arXiv.org/abs/gr-qc/0110034
Title: Introduction to Modern Canonical Quantum General Relativity
Author: Thomas Thiemann
Comments: 301 pages, Latex; based in part on the author's Habilitation
Thesis "Mathematische Formulierung der Quanten-Einstein-Gleichungen",
University of Potsdam, Potsdam, Germany, January 2000; submitted to the
on-line journal Living Reviews.
Abstract: This is an introduction to the by now fifteen years old research
field of canonical quantum general relativity, sometimes called "loop
quantum gravity". The term "modern" in the title refers to the fact that
the quantum theory is based on formulating classical general relativity
as a theory of connections rather than metrics as compared to the original
version due to Arnowitt, Deser and Misner. Canonical quantum general
relativity is an attempt to define a mathematically rigorous, non-
perturbative, background independent theory of Lorentzian quantum
gravity in four spacetime dimensions in the continuum. The approach
is minimal in that one simply analyzes the logical consequences of
combining the principles of general relativity with the principles
of quantum mechanics. The requirement to preserve background independence
has lead to new, fascinating mathematical structures which one does not
see in perturbative approaches, e.g. a fundamental discreteness of
spacetime seems to be a prediction of the theory providing a first
substantial evidence for a theory in which the gravitational field acts as a
natural UV cut-off. An effort has been made to provide a self-contained
exposition of a restricted amount of material at the appropriate level
of rigour which at the same time is accessible to graduate students with
only basic knowledge of general relativity and quantum field theory on
Minkowski space.
Next, these books are a bit dated, but still VERY helpful...
everyone learning loop quantum gravity should get ahold of them:
Rodolfo Gambini and Jorge Pullin, "Loops, knots, gauge theories, and
quantum gravity", Cambridge U. Press, Cambridge, 1996.
Abhay Ashtekar, New Perspectives in Canonical Gravity, Bibliopolis,
Naples, 1988.
By the way, Ashtekar's book is a bit hard to find. Amazon claims
it's out of print, but this other bookstore claims to sell it for a
mere $29.95:
http://www.allbookstores.com/book/8870881849
I don't know if you can trust them. I got lucky: Ashtekar simply
gave me a copy.
>I would also appreciate any pointers to good textbooks dealing with the
>physics that is assumed in the subject. To give you an idea of my level, I
>have graduate-level QFT, I've done 3+1 decompositions of GR and the
>Wheeler-de Witt equation, but I've not heard of spin connections or Wilson
>loops before, for example.
You can get a quick basic introduction to the spin connection from
Wald's introduction to general relativity, but there's a *much* more
detailed treatment in Ashtekar's book. You can read a lot about Wilson
loops in Gambini and Pullin's book.
For spin networks, try this:
Seth Major, A spin network primer, Am. J. Phys. 67 (1999) 972-980,
also available as http://www.arXiv.org/abs/gr-qc/9905020
Finally, here is a reading list which lists books on various topics
that are prerequisites for loop quantum gravity:
http://cgpg.gravity.psu.edu/archives/pubs/readinglist/readinglist.html
and here is a nice review article on applications of loop quantum
gravity to black holes and the big bang:
http://www.arXiv.org/abs/gr-qc/0112038
Title: Quantum Geometry and Gravity: Recent Advances
Author: Abhay Ashtekar
A lot of recent work on loop quantum gravity has drifted into
the neighboring subject of "spin foams". I can list review articles
for this subject too if you're interested in it, but it's a bit hard
to fully understand it without first understanding a bit of loop
quantum gravity first.
Charles Cagle
In article <bclj2g$a87$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu>
wrote:
> The term "modern" in the title refers to the fact that the quantum
> theory is based on formulating classical general relativity as a
> theory of connections rather than metrics as compared to the
> original version due to Arnowitt, Deser and Misner.
What do you mean 'connections'. Connections of what? And how are they
connected?
Loops? Loops of what?
Charles Cagle