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Apr24-10, 04:15 AM
Sci Advisor
P: 5,464
In the meantime I studied the paper in more detail (but not all references Rovelli cites :-)

It seems that he leaves - at some stage - the standard road from classical to quantum theory behind and claims that a certain mathematical model (spin-network Hilbert space, scalar product, ...) is the correct setting for QG. Rovelli leaves behind the idea that spin-foams are just quantum histories of spin networks; nor does he insist on the embedding of a graph in a manifold; he just uses these spin-networks as in- and out-states in rather a standard QFT setting to sandwich certain observables.

This view is supported by the fact that different research programs including the canonical approach seem to "converge" to this general spin-network framework, not necessarily a unique one, but rather closed to some "final theory". So all the old ideas of Ashtekar variables, loop space, cylinder fiunctions, ... are no strict derivation but only a motivation (it is a derivation of the kinematical framework, but not of the whole dynamics of the theory).

Doing calculations his focus is - as exact solutions are not available - on semi-classical or coherent states. Rovelli's aim is to study their physical consequences in certain regimes.

As usual Rovelli closes a review paper with a section regarding the main open question. I always appreciate these conclusions as they sometimes provide more insight than detailed technical calculations. You do not only learn about the current status - but you understand his objectives for the still ongoing research program. Unfortunately the big conceptual issues are hidden between rather technical statements:
- is it possible to construct a Hamiltonion in the canonical approach that matches to the new-look LQG approach? if not, why?
- how does one construct physical observables?

He mentiones a few problems - closely related to each other - which are not only "minor variations" of the framework:
- what is the nature of the cosmological constant? can it be derived from the theory or is it just an input parameter?
- what about q-deformations of SU(2)?
- what about the nature of the Immirzi-parameter?

So what do you think: what are the top-5 questions in LQG as of today?