Spinfoams as a form of quantization?

[Coin]

So this is sort of a belated response to some comments that were made in here over the last couple weeks and that I've been thinking about since.

In the thread about the Lisi article in the New Yorker, Mtd2 and Kea were asking Garrett about whether he is still using a "superconnection" and how he intends to go from there to actually answering questions about the standard model, and eventually he responded:

My guess is that the superconnection will be quantized as a kind of spin foam.

There was another statement I unfortunately can't find which I believe Marcus made at about the same time (maybe it was this?, I think it may have been something about the Friedel work concerning feynman diagrams and spinfoams) that made it at least sound like spinnets/spinfoams can be the basis of a quantum theory even separately from the QG case specifically.

These uses of the term "spinfoam" were a little confusing to me. In my previous attempts to understand spinfoams, I had gotten the impression that spinfoams were something that was derived from loop quantum gravity-- something along the lines that when you look at the wilson loop representation of quantum gravity, and then cut down the space of states by identifying those states which are equivalent under diffeomorphism invariance, the structure that remains is described by spin networks; the evolution of these spin networks in "time" produces spinfoams. Right? And although I know spin networks had been around for a long time before this link with LQG was discovered, as far as I knew LQG was the origin of using spinnets/spinfoams as the basis of a quantum theory, my understanding is before that spinnets were only used in speculative models of combinatorial spacetime.

Now though I am seeing some statements which make it sound like there's more to spinnets than this, and I am curious exactly how deep this rabbit hole goes. Can anyone explain:

1. What exactly does garrett mean that his superconnection could be quantized "as a spin network"?

2. Is there some generic sense in which we can say thing things, potentially things other than the spacetime fabric, can be quantized "as" spinfoams? Or is the sense in which Garret speaks above peculiar to connections and/or superconnections?

(I also should probably stop to make sure I understand what a "superconnection" is in the first place. Would I be correct in saying this is just a connection where the lie algebra of the connection happens to be a supergroup? Also is there a difference between "Quillen superconnections" and generic superconnections, or are superconnections just called "Quillen superconnections" because they were first analyzed by Daniel Quillen?)

 

[marcus]

Can anyone explain:
1. What exactly does garrett mean that his superconnection could be quantized "as a spin network"?

2. Is there some generic sense in which we can say thing things, potentially things other than the spacetime fabric, can be quantized "as" spinfoams? Or is the sense in which Garret speaks above peculiar to connections and/or superconnections?
...

Maybe someone else here can but I personally don't think I can explain either #1 or #2 as stated. I don't recall where Garrett ever said something he's working on might be quantized "as a spin network" or even "as a kind of spin network" meaning some extension, some new kind. I think I remember him saying
"as a kind of spin foam", which is how you quoted earlier. That's very different!
To me that suggests he's guessing at a major innovative step as regards spinfoams--as yet indefinite. We'll see how good the guess is.

The connection between spinfoam and spinnet approaches to QG is highly nontrivial. for ten years there was no logical bridge---no proof of consistency. roughly from 1996-2006 people worked on spinfoams without being sure of a bridge to the other approach. they were using BC spinfoams, now those have been dropped and there is a contest between replacing them with FK spinfoams or EPR type. Now there are indications that one or the other is consistent with the older spinnet approach---at least being able to reproduce some results. But if you choose FK spinfoam you might find you get a slightly different version when you project down. Maybe FK is better in some sense and will win, but if so this might force a slight correction in the spinnet version you project down to or have as the initial and final states of the spinfoam. Since 2006 there has been a lot of change, and also conflict of ideas, in the field. I think you probably know this.

I think anyone who wants to think about spinfoam should probably read parts of the most recent Laurent Freidel paper. It favors the FK (Freidel-Krasnov) version but it is also the closest thing I can think of to a recent REVIEW paper:

http://arxiv.org/abs/0806.4640
Path integral representation of spin foam models of 4d gravity
Florian Conrady, Laurent Freidel (Perimeter Inst. Theor. Phys.)
29 pages, 6 figures
(Submitted on 28 Jun 2008)

"We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks."

==========================

You are interested in how QG approaches can combine matter with geometry----treat matter and microscopic quantum geometry as the same thing. People sometimes mention work by Freidel and Livine in the 3D case around 2005. hep-th/0502106
The Ponzano-Regge Model Revisited III: Feynman Diagrams and Effective Field Theory.
At least for me the point there was that it was in 3D and not 4D---it raised hopes that they could get something in 4D but then quite a long time elapsed.
There were some followup papers (e.g. hep-th/0512113) saying more about the 3D case, which you can track down if you want.

Also mentioned are some fascinating papers by John Baez and collaborators at about the same time, such as gr-qc/0603085 Exotic statistics for loops (strings) in 4D BF theory. the original version v1 said loops and v2 said strings. But no followup to speak of until the recent paper by Winston Fairbairn that you mentioned http://arxiv.org/abs/0807.3188 On gravitational defects, particles and strings.
==========================

Coin, let me tell you what I think myself now, instead of trying to interpret bits of conversation from others. I think you should look at the Conrady Freidel paper I mentioned and especially the last paragraph of the Conclusions, on page 21.

We expect that the path integral representation of this paper could be helpful in further exploring the physical
properties of spin foam models. It could provide a complementary approach to problems that are difficult to deal with
in the dual spin foam representation. A first step in this direction will be made in a companion paper [27], where
we analyze the variational equations of the action and their solutions. Another problem that we have in mind is the
derivation of propagators and Feynman diagrams [36, 37]. We know from lattice gauge theory that perturbation theory
is relatively straightforward in the path integral representation, but only poorly understood in the dual representation
[38]. For the same reason, the path integral of gravity models could provide an easier access to graviton scattering
than the dual spin foam sum.

 

[marcus]

In other words, Coin, even though you asked about spinfoams as an approach to quantization if you take a hard look at where QG (and Loop QG in particular) is going you may decide you should keep an eye on path integral as an approach to quantization.

You have both Loll and Freidel working on that approach.

At the Sydney GR18 meeting in 2007 (600 people, I think, a triannual international GR meet) you had exactly TWO invited speakers talking about Quantum Gravity, and they were Loll and Freidel. http://www.grg18.com/

Ashtekar was elected president of the professional organization behind the GR conferences, and Bojowald was awarded a prestigeous prize for his quantum cosmology (applied QG) work. But the invited speakers on QG were Loll and Freidel. So it is a straw in the wind.

Maybe Garrett Lisi was not speaking all that definitely in that instance, maybe he just meant some kind of quantization that QG researchers use---maybe at some level there is no difference between spinfoam and path integral. I can't say. I just wouldn't develop tunnelvision and get locked into one concept of what was meant or being talked about.

Loll's approach is very clearly and explicitly path integral from the git-go. for an introduction see my favorite SciAm article, the link is in my signature.

 

[marcus]

Coin you mentioned some discussion by me, which you couldn't find (it wasn't the Fairbairn thread you mentioned, evidently). It may have been this:
https://www.physicsforums.com/showthread.php?p=1791346#post1791346

The Conrady Freidel paper was Francesca's pick for the MVP (most valuable paper) second quarter of 2008. Francesca is an insider (she and Carlo Rovelli recently co-authored a paper on quantum cosmology.) I had some discussion of the Conrady Freidel work there.

I have an abstract of the next Conrady Freidel paper there----it was presented at the QG2 conference in July but has not yet been posted. We only have the abstract. It shows where they are going after the one you saw.

It is of incalculable importance to have a path integral formulation.

Something to keep in mind is that the PATH is the spacetime. A spacetime is a way of getting from initial to final space geometry-----from space geometry state A to space geometry state B.

As in the original Feynman path integral, where the path is that of a particle, the spacetime, a path thru spatial geometries, can be very wild and erratic. But one has an action defined on paths and one can (quantum) average them up and get a smooth classical result.

I have to go----supper. Cant edit this. But wanted to get the idea out that in this kind of path integral the quantum spacetime geometry itself is the path.

amazing to see Conrady and Freidel actually get an action defined. Check it out.
not impossible that matter could be added to this! or that Lisi could find an entry point there.

 

[Fra]

made it at least sound like spinnets/spinfoams can be the basis of a quantum theory even separately from the QG case specifically
...
Now though I am seeing some statements which make it sound like there's more to spinnets than this, and I am curious exactly how deep this rabbit hole goes.

I can't explain anything, but I can just say that similar thoughts has intrigued me as well. It was something like this that I expected to find when I ordered Rovelli's book on QG, but during the development he doesn't seem to go the expected direction.

But while I know nothing of Lisi Garrett's ideas I intuitively think there is something beyond this, that could possibly be thought to address also some very fundamental question of quantum mechanics, and provide a path to unification at the same time.

I'm definitely tuned into these things.

My personal association starts with distinguishable states, defining the observers state of information, and this can be thought of also as microstructures, and very loosely a way a spin network can be thought of as a kind of microstructure. And considering uncertain microstructures and microstates the spin-foam concept seems conceptually in reach. I suspect that if this is done right, we might not need to apply a "quantization procedure" in the ordinary sense, because the quantum nature might come naturally from the evolving the uncertainty.

But this connection to the spin networks stuff is far from clear to me. I was hoping that Rovelli's book would provide me some answers, but as far as I can understand, it doesn't. I consider this lead pretty hot. I'm tuned into see what comes up on this.

/Fredrik