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With any luck, sometime soon you can read this paper on the arXiv:

Aristide Baratin and Laurent Freidel

Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams

The idea is that any ordinary quantum field theory in 4d Minkowski spacetime can be reformulated as a spin foam model. This spin foam model is thus a candidate for the G -> 0 limit of any spin foam model of quantum gravity and matter!

In other words, we now have a precise target to shoot at. We don't know a spin foam model that gives gravity in 4 dimensions, but now we know one that gives the G -> 0 limit of gravity: i.e., ordinary quantum field theory. So, we should make up a spin foam model that reduces to Baratin and Freidel's when G -> 0.

The fascinating thing I noticed is that their spin foam model seems to be based on the Poincare 2-group. I invented this 2-group in my http://www.arxiv.org/abs/hep-th/0206130" [Broken]. The physical meaning of their spin foam model was unclear, and some details were not worked out, but it was very tantalizing.

I now conjecture - and so do Baratin and Freidel - that when everything is properly worked out, Crane and Sheppeard's spin foam model is the same as Baratin and Freidel's. So, it gives ordinary particle physics in Minkowski spacetime, at least after matter is included (which Baratin and Freidel explain how to do).

If this is true, one can't help but dream...

... that deforming the Poincare 2-group into some sort of "quantum 2-group" could give a more interesting spin foam model:

Of course this dream sounds "too good to be true", but there are some hints that it might work, to be found in http://arxiv.org/abs/hep-th/0501191" [Broken]. In particular, they describe gravity in way (equation 26) which reduces to BF theory as G -> 0.

Optimistic hopes in quantum gravity are usually dashed, but stay tuned.

Aristide Baratin and Laurent Freidel

Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams

The idea is that any ordinary quantum field theory in 4d Minkowski spacetime can be reformulated as a spin foam model. This spin foam model is thus a candidate for the G -> 0 limit of any spin foam model of quantum gravity and matter!

In other words, we now have a precise target to shoot at. We don't know a spin foam model that gives gravity in 4 dimensions, but now we know one that gives the G -> 0 limit of gravity: i.e., ordinary quantum field theory. So, we should make up a spin foam model that reduces to Baratin and Freidel's when G -> 0.

The fascinating thing I noticed is that their spin foam model seems to be based on the Poincare 2-group. I invented this 2-group in my http://www.arxiv.org/abs/hep-th/0206130" [Broken]. The physical meaning of their spin foam model was unclear, and some details were not worked out, but it was very tantalizing.

*What did it mean?*I now conjecture - and so do Baratin and Freidel - that when everything is properly worked out, Crane and Sheppeard's spin foam model is the same as Baratin and Freidel's. So, it gives ordinary particle physics in Minkowski spacetime, at least after matter is included (which Baratin and Freidel explain how to do).

If this is true, one can't help but dream...

... that deforming the Poincare 2-group into some sort of "quantum 2-group" could give a more interesting spin foam model:

*ideally, something that describes 4d quantum gravity coupled to matter!*This more interesting spin foam model should reduce to Baratin and Freidel's in the limit G -> 0.Of course this dream sounds "too good to be true", but there are some hints that it might work, to be found in http://arxiv.org/abs/hep-th/0501191" [Broken]. In particular, they describe gravity in way (equation 26) which reduces to BF theory as G -> 0.

Optimistic hopes in quantum gravity are usually dashed, but stay tuned.

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