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 neccessary 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 wont 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.
SU(2) is a "real" group. Its parameters are three real numbers. e.g. a unit vector and an angle of rotation. Just as SO(3), except that the angle runs not from 0 to 2pi but from 0 to 4pi.
SU(2) doesn't give you the evolution in the fourth dimension it gives you the rotations in 3 dimensions...
Well it is based on representation theory and no it's not always discrete.
SO(4) ~ SU(2)*SU(2) Thus a theory based on SO(4) representations will naturally have half integer labels. SO(3,1) has an SU(2) subgroup, but the original BC model didn't use that but "simple" representations those are...
I discussed these results with Mikovic a while ago, they are not incompatible with the positive results in the new vertices. It's crucial to understand that he is talking about old fashioned LQG not about the idea to define the dynamics using spin foams.
I don't recall the technical details...
You missed my point. I know all this. First of all look at the EPRL papers. The second class constraints are NOT implemented as C|phys> = 0 but as <phys|C|phys> = 0. This is another of the standard techniques to deal with them. Or rather in the papers from a few years back several options are...
The second class constraints are treated differently in the EPRL model (via expectation values or Master Constraint type considerations), his complaint is IIRC that the symplectic structure is wrong.
Anyhow Spin foam "quantisation" is not a quantisation in any standard meaning of the word...
The best reference for spin foams on CW-complexes rather than on triangulations is Oeckls:
http://arxiv.org/abs/hep-th/0110259
and his book especially.
More recently KKL rediscovered this and applied it to the EPRL spin foam models:
http://arxiv.org/abs/0909.0939
Triangulations...
apeiron, John Baez has argued along these lines, that instead of trying to unfiy it to a simple symmetry and then having to contend with an ugly (often unnatural) breaking process we should look for mathematical structures that contain this group naturally.
Yeah that makes more sense. So what you are saying is, if I treat the magnetic field as an external source which doesn't transform under P, then P is broken. Right? That is pretty nonsensical from a fundamental physics perspective but from a phenomenological perspective it does make sense to...
I guess you mean for static magnetic fields only? What about magnetic fields in an EM wave? Those can be consistently considered in a closed system without sources after all. as the QED vertex is P invariant that would mean parity would be spontaneously broken by EM radiation, right?
True, I shouldn't trustmy memory on stuff I don't work with. I wonder what it was I was remembering... Possibly magnetic monopoles? Would that mess with parity?
No, it is like having a preferred orientation in space. Which is exactly what P is. As charges know about orientation of space via the cross product in the Lorentz Law, already classical EM violates P, but not CP.
Thus CPT says (roughly, heuristically) that there is no preferred orientation...
To flesh out eteras answer a tiny bit: The V_0 representation is the trivial representation thus every group element is represented as the identity on it. The other observation you need is that acting on the left with any group element can be absorbed into a reparametrisation of the integral...
saltlick if you can only move in one direction in that dimension it doesn't really make sense to speak of untying a 4D knot, right?
The prove you look for is elementary so I don't know where to find it. If you look at the two dimensional projection of the knot distinguishing over and under...
jal, I don't understand your question. Marcus, I was organizer so I didn't necessarily get a good overview of what's happening scientifically.
There are as far as I see three major fronts: The mathematical front, the model front and the observational front. This does not include dynamical...
Re the name, I doubt it. There is an active group in Beijing hosting it, I know of no online information yet, it's a bit early for that.
My point was that the quantization of geometry the mathematicians like is somewhat different from what physicists mean with quantization. I don't think the...