How Significant Are Bonzom's Contributions to Loop Quantum Gravity?

[marcus]

I have been tardy in realizing the interest/significance of some 2011 and 2012 papers co-authored by Valentin Bonzom with various people (Alok Laddha, Rivasseau, Livine, Gurau, Smerlak,...). Maybe some others here have been more alert and seen this already. I simply want to rectify the situation and focus some attention in an attempt to catch up.

What woke me was the January 2012 paper 1201.4996 of Bonzom and Smerlak, which solves several problems in the spinfoam approach by extending quantization to the rest of the cell complex.
This uses intriguing math devices of the discrete exterior derivative, discrete (de Rham, cochain) complex which are already described in the March 2011 paper 1103.3961 by the same authors.

But while co-authoring these two seemingly important and innovative papers Bonzom was busy with quite a few other papers as well, on diverse subjects. So instead of citing separate ones individually at this point, I will just give a single link to all of them.
http://arxiv.org/find/grp_physics/1/au:+Bonzom_V/0/1/0/all/0/1

His PhD thesis (September 2010, Marseille) is included there. There are 23 papers of which 13 are from 2011-2012.

 

[marcus]

It's not certain that the Bonzom Smerlak 1201.4996 paper actually is the breakthrough which it seems to be at first sight. It definitely could be, but I can't be sure yet.

They have a longer paper coming out. The present one is just a letter: 5 pages or 6 including references. Their reference [18] is Cellular quantization of discrete BF theory to appear.

The longer paper can be expected to supply more detail and should be quite interesting. A key issue for me is whether I should think of the region whose quantum geometry is studied as a FOURBALL WITH BOUNDARY or alternatively as S³ x I, the 3-sphere cross an interval. I guess the interval could be finite or infinite, could be the whole real line.

Talking about the paper with other people who have read it would be a help. I want to hear other people's ideas about it.

It could be that Bonzom Smerlak's work is only interesting in the case where if you take a spatial slice of the world has nontrivial topology like a 3-sphere so for instance is BOUNDARYLESS like a 3-sphere.

The other case is where you have a "solid" chunk of spacetime with boundary and you take a slice which is again a bounded chunk (but of space this time), topologically speaking a 3-ball with boundary---a familiar solid ball of 3d space. Topologically simple, except it does have a the additional complication of a boundary.

After talking to other people (not enough) I begin to think that if this topologically trivial case is the interesting one then maybe Bonzom Smerlak's results don't get us anywhere, or even might not apply. Not sure though.

On the other hand if our chosen typical space is boundaryless, like a 3-sphere, then I suspect their results do apply and may even do some nice things for us.

Here's the link, in case anyone wants to read and help understand the paper:
http://arxiv.org/abs/1201.4996