We should probably have a QG thread focused on the work of the Uruguayan physicist Rodolfo Gambini and his co-workers, such as Jorge Pullin (LSU) and Rafael Porto (Carnegie-Mellon) and others. I will get some links. I would like to understand better how Gambic QQ fits together with more familiar types of Loop QG as done by Ashtekar, Rovelli, Smolin, Thiemann, Bojowald .... We are lucky at PF because someone (a grad student i think) in contact with Gambini group has visited PF and written us some posts. But we have to develop our own base of knowledge because grad students normally have only limited time for message boards. the first thing I notice may seem superficial to some people, but I think it is significant: someone on the team is a better than average writer. If you grab a Gambini, Pullin, et al paper out of archiv, chances are it will be more than average clear and concise. another thing is that Michael Reisenberger, whose most recent 3 or 4 papers were co-authored with Rovelli, is currently in Uruguay----and also note that Gambini most recent paper is Consistent discretizations and loop quantum geometry which says explicitly that it is building a bridge between the CD approach and LQG. So IMHO we should look at the CD approach and see what is special, what it offers, and how it have some common ground and might fit together. As a watcher (not a participant) I think one should check this out. Maybe some time Rovelli and Gambini will find something in common and write a joint paper, who knows? As a side comment, Ashtekar's most recent paper (Gravity and the Quantum) mentioned Gambini-group's hamiltonian as an alternative to Thiemann's hamiltonian. this was at the top of page 20. ----quote Ashtekar--- A key open problem in loop quantum gravity is to show that the scalar/Hamiltonian constraint---either Thiemann’s or an alternative such as the one of Gambini and Pullin---admits a 'sufficient number' of semi-classical states. Progress on this problem has been slow because the general issue of semi-classical limits is itself difficult in any background independent approach (12). However, a systematic understanding has now begun to emerge and is providing the ‘infrastructure’ needed to analyze the key problem mentioned above [38, 52]. ---end quote--- Well actually Gambini and Pullin are proposing more than just an alternative to the various LQG hamiltonian constraints, they have a way of avoiding the constraint equation. they introduce a very-small-step unitary evolution operator. I hesitate to call this "time"-evolution. because time is such a loaded word that the minute () one says it one is swept away in a tide of confusions. but for better or worse they got rid of the damned hamiltonian constraint and they have this very-small-step discrete evolution operator which maybe will turn out to be legitimate (!) who knows? Personally I like zig-zags in the development of physical theory because of the comedy and unexpectedness. The Gambini-group line of research has the potential to add a surprise element and make the story more interesting. So I want to learn more about this.