the thing to focus on is a relatively recent formulation of Lqg called "covariant Lqg". If I google that, I get:How is loop quantum gravity related to the principle of relativity, in particular to the diffeomorphism invariance of general relativity?
You might be interested in a series of work by Jonathan Engle. Here is the most recent.How is loop quantum gravity related to the principle of relativity, in particular to the diffeomorphism invariance of general relativity?
Thanks for that Marcus. I splashed out and ordered a copy and also downloaded it. I really enjoy reading anything by Rovelli.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
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.