marcus said:
thanks!
So it's a Jan 2008 lecture series.
The formulation has changed some since, which could matter. There is EPRL and variations like Jon Engle's.
I don't know if it would make a difference to you but you might be interested in looking at some of the more recent papers I linked to.
e.g. in post #4
http://arxiv.org/abs/1303.4636
Now the standard textbook on LQG is "Covariant LQG" (2014) by Rovelli and Vidotto. There is a free draft version one can download or one can buy the book. I gave a link. It's different from what was current in 2008.
http://www.cambridge.org/us/academi...roduction-quantum-gravity-and-spinfoam-theory
Thanks for that Marcus. I splashed out and ordered a copy and also downloaded it. I really enjoy reading anything by Rovelli.
The theorem, called LOST, that reduces the diffeo invariant states to one unique state is quite generally applicable, though I am not sure how covariant LQG handles it specifically.
LOST is discussed in this interesting paper by Ashtekar where he talks about 'diffeomorphism covariance' which is a term I'm not familar with so not sure if it relates. (I see I spelt his name wrong again in my previous post!)
http://arxiv.org/abs/0904.0184
"Some surprising implications of background independence in canonical quantum gravity" by Abhay Ashtekar
Abstract:
"There is a precise sense in which the requirement of background independence suffices to uniquely select the kinematics of loop quantum gravity (LQG). Specifically, the fundamental kinematic algebra of LQG admits a unique diffeomorphism invariant state. Although this result has been established rigorously, it comes as a surprise to researchers working with other approaches to quantum gravity. The goal of this article is to explain the underlying reasons in a pedagogical fashion using geometrodynamics, keeping the technicalities at their minimum. This discussion will bring out the surprisingly powerful role played by diffeomorphism invariance (and covariance) in non-perturbative, canonical quantum gravity."
P3:-
" The first goal of this article is to show, by a careful analysis of the WDW theory, that there is in fact no tension. We will see that there are apparently surprising results also in the WDW theory; diffeomorphism invariance is a much stronger requirement that one might have first thought. Results can seem counter intuitive if one does not carefully distinguish between the kinematical algebra and the algebra of diffeomorphism invariant variables. The second goal is to provide intuition for the origin of the two features of the kinematics of LQG which are not shared by familiar Minkowskian quantum field theories —the non-separability of the kinematical Hilbert space and the non-existence of a local connection operator Aia(x).
We will see that they can be traced back to the diffeomorphism covariance of LQG. Finally, it will be instructive to compare the role of gauge invariance in the Maxwell theory with that of diffeomorphism invariance. We will find that, because of its inherent non-locality, diffeomorphism invariance is much more powerful than gauge invariance." (my bold)
There appear to be some who find the LOST theorem to be too restrictive:-
https://golem.ph.utexas.edu/string/archives/000990.html
" The first part of today’s paper explains all this and shows that the difference in the treatments can be summarised by saying that the usual Fock space quantisation of the string uses a Hilbert space built upon a covariant state whereas the loopy approach insists on invariance of that state which is a much stronger requirement.
My point is that covariance is the property which is physically required (and in fact states in the classical field theory are covariant but not invariant) and thus statements like the LOST theorem have too strict assumtions."
Both of these papers are over 5 years old so this issue may already be resolved. I couldn't find anything more recent though.
