The “math kids” are hard at work. http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.3892v1.pdf Spin foam model from canonical quantization Sergei Alexandrov 26 may 2007 ----------- A quick search of dual 4-simplex found this supplementary information http://www.valdostamuseum.org/hamsmith/FynCkb.html 4-dim HyperDiamond Lattice ------------ http://www.fogandonions.com/index.html PHYSICS: Projective Structures, Mass Generation ------------------ http://graphics.idav.ucdavis.edu/research/mat_bou_sur Material Boundary Surfaces ------------------- If you can follow all of that math then you don’t need to look at a simple version, without math., the pictures in my blog. jal
You've spotted a significant development. He hasn't got a formula for the Lorentzian spinfoam vertex amplitude yet but he is clearly working hard on it. He cites the recent Rovelli et al paper, discusses it quite a lot. That is his reference [24] which you see all thru the latter half of his paper. Rovelli et al dealt with the Euclidean case which is like a first stage. I think a number of people besides Sergei Alexandrov could be expected to take up the challenge of getting to the next stage. Your link is to the PDF so I will add one here to the abstract in case anyone just wants a quick look at the summary. http://arxiv.org/abs/0705.3892 Spin foam model from canonical quantization Sergei Alexandrov "We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model."
The two senior people at Montpellier II are Eric Buffenoir and Philippe Roche, I think there is also Karim Noui there. The 2004 Loops and Spinfoam conference at Marseille was organized by Rovelli and Roche. Alexandrov got the PhD at Paris around 2004, then he went to Utrecht for postdoc, now he is at Montpellier II. One could say there is a GROUP there who can do significant covariant LQG and spinfoam research if they choose. All these people have impressive research records already. have to go, will think about this some more later. there is a network of 3 universities Lyon, Montpellier, and Marseille. Etera Livine is at Lyon, there is that group at Monpellier, and there are Rovelli and Perez and their group at Marseille.. In this research network, they know each other and are accustomed to work together. suddenly, just in the past 3 or 4 weeks we get 3 papers about the spinfoam vertex one from Lyon (Livine and Speziale) one from Rovelli et al at Marseille, and one from Montpellier.
to correct a mistake: I am told that Karim Noui is now at Tours. so there are some four French universities with research cadres in Quantum Gravity forming a kind of network. Marseille (Rovelli, Perez et al) Monpellier (Roche, Buffenoir, Alexandrov) Lyon (Livine, Speziale, and also Freidel when he is not at Perimeter) Tours (Noui) the focus seems to be on the spinfoam path integral approach.