Lewandowski et al's generalized spinfoams

[tom.stoer]

There are several incompatibilities between Loop Quantum Gravity (LQG) and spin-foam models (SFMs).
The first difference ... LQG is aquantum theory of gravitational field with all its local degrees of freedom. This is not a discretized theory. ... The SFMs on the other hand, are quantizations of discretized classical theories.
Secondly, LQG is a diffeomorphism invariant theory of fields on manifolds. ... The SFMs, on the other hand, are theories of piecewise flat geometries defined on piecewise linear manifolds. ... In order to match the two theories, either LQG should be restricted to the piecewise linear manifolds and piecewise linear spin-networks, or SFMs should be suitably generalized.
The third difference ... In the LQG canonical framework, ... there is no justified way to restrict the graphs to those dual to triangulations of the underlying 3-manifold. The SFMs on the other hand, use only simplicial complexes ... and the spin-networks defined on their boundaries. Therefore they do not define a spin-foam history of a generic spin-network state of LQG. In particular, LQG admits knotted and linked graphs. The simplicial SFMs do not allow such states as well as they do not allow graphs with vertexes more then 4-valent.

I think (3) is the main issues to be addressed in order to establish a link between LQG and SFM. Anyway - even after having studied the paper which claims to resolve (3) and (2) I am not sure if this helps to overcome all LQG ambiguities.

 

[marcus]

Jerzy Lewandowski gave an introductory presentation of embedded spinfoams
at the June 2009 Abhayfest (where also Rovelli, Freidel, and Smolin gave talks.)
The slides are hand-drawn and resemble colored felt-tip sketches on a whiteboard or transparency sheets.
They including his rough pictures (such as any mathematician might draw when explaining.)
http://gravity.psu.edu/events/abhayfest/talks/Lewandowski.pdf

For me it was a congenial presentation. Here is the sound-track:

http://gravity.psu.edu//~media/abhayfest/Lewandowski.rm

The whole menu of talks is here:
http://gravity.psu.edu/events/abhayfest/proceedings.shtml

 

[marcus]

Today Lewandowski and his collaborators posted the follow-up paper to the September 2009 one that this thread is about. I quote from a post by MTd2, who highlighted a part of the abstract which I don't yet fully understand.

...

http://arxiv.org/abs/0912.0540

The EPRL intertwiners and corrected partition function

Wojciech Kamiński, Marcin Kisielowski, Jerzy Lewandowski
(Submitted on 3 Dec 2009)
Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective in the general n-valent vertex case for the Barbero-Immirzi parameter less then 1. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.

 

[MTd2]

Ive been trying to think about the highlighted part, and I guess it is just like that. For immirzi smaller than modulus 1, EPRL is merely a necessary description, but is not sufficient at all. One needs spin foams described by much more complicated foams than that.