Hi tom.stoer,
I personally don't think of spin foams as arising from a quantization construction via simplicity constraints, see the first half of my paper with Bianchi for example. So I never paid too much attention to those results.
And indeed I would interpret them to show that they are not...
Quick answers: Yes D depends on \gamma. The solution spaces should differ, but be isomorphic/code the same geometry, and yes, we already have a perfectly good spin foam model: FK without \gamma is what is favoured by our analysis.
The caveat is that not all technical lemmas are available for...
Hi marcus, I'm glad you thought my talk was clear, I'm afraid I was quite dissatisfied with it myself. For one, I didn't properly anticipate how difficult it would be to describe the underlying geometry without pointing at the slides, for two I was quite sick during it. Only propped up through...
Thought some people here might enjoy a little video we made:
For context: Everybody involved in this project, in front of and behind the camera, is actually a theoretical physicist. This should obviously be taken as tongue in cheek, and it is not directed against string theory in...
So I will try to keep this brief, with just a few counterpoints...
These proposals only give us a framework to discuss cosmology, we do indeed agree on the framework (and my paper explicitly uses the no-boundary proposal) but within that framework I still must insist on the very physical...
Good question. The idea is that we allow any boundary data, possibly subject to some constraints that are considered "kinematical". The dynamics then implement the rest of the constraints, giving the overlap of the boundary state with the physical states. By conditioning this amplitude...
It is certainly necessary to restrict the class of 2-complexes. Otherwise even at the 1-vertex level you can construct arbitrarily many divergent 2-complexes. The most plausible such restriction I've seen this far is this:
http://arxiv.org/abs/1107.5185
As for your second question, you...
I think that is wildly optimistic, to say the least, I am not sure anybody really expects the limits to exist as such, and while it's possible to calculate with the theory the physical meaning of these calculations is very much subject to a lively debate in the community. I wrote the paper on...
I think you are exaggerating the situation somewhat. If you do a pure string PhD you won't find switching fields all that easy either. It really depends where you're looking at. If by physics you mean particle physics, especially in the context of high energy experiments then yes.
But physics...
Given that many people in the community are collaborating with Rivasseau and other QFT experts you can rest assured that many are well familiar with things beyond. For example Rovelli and collaborators have looked at whether the fermion coupling to gravity through the vielbein is sensitive to...
The SU(2) is the local group. Each node of the network has its own SU(2) invariance. each link its own SU(2) matrix in the spin-j representation.
Spins are the representations of SU(2), they are quantized because SU(2) is a compact group. If you build models with other local groups you get...
Sure, it's mathematically important, but not in the physics/geometric interpretation of the state sum.
More important is the Hopf Bundle:
http://en.wikipedia.org/wiki/Hopf_fibration
Roughly speaking you have S^3 as a bundle with fiber S^1 over S^2. Since the phase S^1 doesn't matter so much...
This isn't really how we use it though. The isomorphism SU(2) - S^3 doesn't really play a strong geometric role in the models considered.
Remember that the Ponzano Regge model based on SU(2) describes flat 3-space.
So? The first thing you describe seems to be SU(2) \times R^4.
The double cover can be seen in many ways, I like the geometric picture of SO(3) as a ball of radius pi with antipodal on the surface of the ball identified.