Questions on Freidel's Group Field Theory (hep-th/050516)

[selfAdjoint]

Questions on Freidel's "Group Field Theory (hep-th/050516)"

In Laurent Freidel's general description of group field theory, http://arxiv.org/abs/hep-th/0505016" , which I am studying as preparation for the paper on getting quantum dynamics out of kinematics which was recommended by Helge Rose', I have hit a question. So in case others may want to follow this course to exciting new results, I pose it here, and dignify it with a thread in expectation there will be other questions.
Freidel says:

There are many examples of such {sc. spin foam} models. Historically, the first example is due to Ponzano and Regge [6]: They showed that the quantum amplitude for euclidean 2 + 1 gravity with zero cosmological constant can be expressed as a spin foam model where the group G is SU(2), the faces are labelled by SU(2) spin jf ... The remarkable feature of this model is that it doesn’t depend on the choice of the two complex F but only on MF

My question is: how far is this invariance due to features of the Ponzano-Regge model and how far is it a combinatorial expression of the lack of local degrees of freedom in 2-D GR? In general how does the combinatorial structure of a spin-foam model relate to the underlying dynamics on the manifold being represented?

 

[Timbuqtu]

I suppose you meant hep-th/0505016, "Group field theory: An overview"?

 

[selfAdjoint]

I suppose you meant hep-th/0505016, "Group field theory: An overview"?

Yes. Quoting from the conclusion:

We will like this letter to be an invitation for the reader to look more closely and further develop the GFT’s as a third quantized version of gravity. As we have argued, in order to insure that these theories effectively encode the dynamics of General relativity one needs to gain an understanding on the action of diffeomorphisms on spin foams
model and its counterpart in GFT, presumably implemented as a renormalisation group. We have discussed so far pure gravity models and a consistent inclusion of matter fields and particles in the GFT framework is clearly needed. Finally, an understanding of the physical meaning and properties of GFT instantons will provides us a window into the
non perturbative physics of these theories.

 

[Kea]

My question is: how far is this invariance due to features of the Ponzano-Regge model and how far is it a combinatorial expression of the lack of local degrees of freedom in 2-D GR? In general how does the combinatorial structure of a spin-foam model relate to the underlying dynamics on the manifold being represented?

selfAdjoint

It is basically a combinatorial expression of the lack of local degrees of freedom. The beauty of Ponzano-Regge was in actually constructing such an expression.

Sorry, but your second question is a little vague to me.
Kea