Every now and then Ashtekar produces a survey like this, an overview with his perspective on where things are going.
BTW here's the link to the abstract:
http://arxiv.org/abs/gr-qc/0410054
Besides being up-to-date----the latest Ashtekar overview---what is special about this one. what tell-tale straws in the wind can be noticed?
1. first there is the context
he is paired off against the string theorist Gary Horowitz
in a special 2005 issue of the New Journal of Physics celebrating the
100th anniversary of Einstein's 1905 papers
the special issue (edited by Jorge Pullin) is called
Space-time 100 Years Later
Here is the URL for the New Journal of Physics:
http://www.iop.org/EJ/njp
I suppose hardcopy of the centennial issue may reach the shelf
at university libraries. It sounds like a book "Space-time a Hundred Years Later", and it might sell as a book. But the primary access is electronic.
So there is a kind of parity in the presentation of String and Non-string
approaches to Quantum Gravity and their different perspectives on what will replace the space and time of General Relativity.
Here's a link to the Gary Horowitz survey of String that Abhay's is paired with in the centennial issue
http://arxiv.org/abs/gr-qc/0410049
2. He emphasizes some work by Rodolfo Gambini (consistent discretizations) that has so-far not been noticed by LQG people so much.
We had someone come here to PF called Edgar1813 who is involved in this consistent discretizations line of research and apparently knows Gambini.
Abhay is sort of like the center player, or the "quarterback" and it is a good thing if he notices someone in a forward position or out on the end. this is only a vague analogy. Anyway I watch for how much notice Gambini, Pullin, Porto etc get in a concise official-stamp-of-approval survey paper.
3. His reference [41] is to the Ambjorn Jurkiewicz Loll paper about their computer Monte Carlo simulations "Emergence of a 4D World..."
To me it is extemely unclear how this simplicial modeling fits together with LQG. but he is including it in his vision of how non-string Quantum Gravity is developing.
4. His references [49] and [50] are to two papers by himself and Bojowald which have not even been posted on the preprint Arxiv yet. they are about what there is instead of a singularity, in black holes, and the LQG picture of how black holes evaporate
there was a strong emphasis on applications, which ultimately lead to observable phenomena. this fall at Ashtekar's institute IGPG there was a series of 3 talks about LQG phenomenology by Parampreet Singh.
the effort is to derive little details about the CMBR---its spectrum of bumps and dips---which could be looked-for. I think Abhay is pushing hard for finding something testable.
another indicator besides the perspective in this survey article you flagged is just the lineup of seminar talks at Penn State----what his IGPG colleagues and visitors and graduate students are giving talks about. Some of the talks are online but most unfortunately are not.
In case anyone has not tried this before, here is the schedule of talks (select "this semester" from menu)
http://www.phys.psu.edu/events/index.html
