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atyy
#5
Aug2-10, 06:25 PM
Sci Advisor
P: 8,535
Quote Quote by marcus View Post
Atyy said something about LQG turning out eventually to be a "limit" of some unknown GFT. That is not quite right because LQG already is a GFT, and not just a limit, it IS that. You don't have to wait for something to happen, or take a limit.
Theories have various different equivalent formulations. The April paper describes various equivalent or convergent formulations of LQG, one being the GFT version.
You may be right, I don't know which way it will go, but I don't think the various formulations Rovelli mentions have been shown to be equivalent or convergent. And in my statement I had in mind canonical LQG.

Among the open problems listed by Rovelli:

13. Find a simple group feld theory [41] whose expansion gives (52).
14. Find the relation between this formalism and the way dynamics can be treated in the canonical theory. ... Can we construct the Hamiltonian operator in canonical LQG such that this is realized?

Furthermore, because I expect GFTs to have to be renormalized, I would say the present work looks at a "low energy" limit of GFT, along the lines of "Finally, if one regards group field theory as fundamental, rather than just a convenient computational tool to arrive at the spin foam vertex expansion, then one is led to take the coupling constant λ as a physical parameter which can run with the renormalization group flow. http://arxiv.org/abs/0909.4221"