Extended idea of diffeomorphism

[marcus]

... recent one by Buffenoir, Henneaux, Noui, Roche
http://arxiv.org/gr-qc/0404041
Hamiltonian Analysis of Plebanski Theory

Buffenoir, Roche, Noui have published some pretty interesting papers to date.
I am trying to understand what their new paper means
in terms of a general picture of quantum gravity

Roche is the co-organizer with Rovelli of the May 2004 Quantum Gravity conference at Marseille.

this paper does not say spin foam in the abstract but I would
think of it as about spin foam, and also knots.

this is a "through a glass darkly" post trying to identify the dim outlines of something

Fairbairn Rovelli emphasized that if you use chunkies then the pure quantum states of space boil down to a countable list of knot-states

(merely using diffeos leaves a lot of slag, or chaff, which they argue is spurious---not physically meaningful)

And Baez has called attention to the star-category idea---something that QM and GR have in common---and this highlights cobordisms

(because nCob and Hilb are both *-categories: that is categories with a
reciprocity pairing among the morphisms)

so if knots are important and cobordisms are important then perhaps 2-knots
are important (equivalence classes of spin foams, under what?)

and who is talking about 2-knots?
well Cattaneo et al, for some.

now Buffenoir et al (the Uni Monpellier people) bring us a new piece to the puzzle that says "hamiltonian plebanski" on it. Past experience of these people suggests that this piece may fit into the picture in an interesting way.

 

[marcus]

here is the start of Buffenoir et al's introduction:

---exerpt gr-qc/0404041----

Plebanski theory [1] is a 4-dimensional BF theory with an additional field which forces the B field to satisfy the simplicity constraint. It contains, as a particular sector, 4-dimensional pure gravity and is therefore an interesting field theory. The quantum properties of this field theory are, however, largely unknown.

One important line of study aims at discretizing this quantum field theory with the tools of lattice gauge field theory leading to spin-foam models.

Although spinfoam models have been the subject of numerous works over these last years (see the introduction [2] and the review [3]), central issues are not understood and the technical tools needed to address these central questions need still to be developed. In particular we had in mind two pressing questions when beginning this work:

-is it possible to compute from first principle the weight of the faces, edges and vertices in the spin foam model description of Plebanski theory?

-can we see the appearance of quantum groups in Plebanski theory with cosmological constant?

The following work is a study of the Hamiltonian description of Plebanski theory. In particular we want to address the following problems:

-computation of the Liouville measure in the path integral expressed in term of the original variables of Plebanski theory. This could be a first step for understanding how to fix the measure of spin foam models.

-computation of the Dirac bracket of all the fields once all second class constraints...

----end quote---

 

[marcus]

...so if knots are important and cobordisms are important then perhaps 2-knots
are important (equivalence classes of spin foams, under what?)

and who is talking about 2-knots?
well Cattaneo et al, for some.

just a brief exerpt from Cattaneo et al, the 1995 paper that Buffenoir et al cite:
----quote, pages 18,19----
As has been mentioned in Section III, the observables associated to a 4-dimensional BF theory must be associated to 2-dimensional surfaces Σ imbedded (or immersed) in the 4-manifold M.
...
...

BF theory in 4 dimensions should provide the right framework for invariants of 2-knots (embedded surfaces) or of singular 2-knots (generally immersed surfaces). Preliminary computations (see [16]) suggest that the expression of these invariants...

---end quote---
http://arxiv.org/hep-th/9505027

 

[marcus]

the main topic of this thread is chunkymorphisms
(homeomorphisms smooth in both directions except at a finite set)
and the LQG hilbert space

and the Fairbairn/Rovelli paper

There turns out to be some follow-up news. F/R posted a revised version of their paper, same arxiv number.
At the end they say that Lewandowski contacted them to tell them that he and Ashtekar had also been thinking along similar lines.

Judging from this second or third hand information, what F/R (in their revised paper) say that Lewandowski said,
it seems that Ashtekar and Lewandowski were also thinking about
chunkymorphisms and perhaps have a paper in the works about it.

maybe the idea has legs

 

[marcus]

Another new paper from Rovelli and others

Carlo Rovelli visited this thread earlier, see for example post #42 on page 2.

the thread initially got started around the Fairbairn/Rovelli paper that appeared this year

now Rovelli has a new paper out
http://arxiv.org/gr-qc/0406063
with Simone Speziale and Daniele Oriti.

I thought I'd mention it

BTW the paper cites some people whose work we've discussed in other PF threads
Jan Ambjorn, Etera Livine, Karim Noui,... to name a few

 

[Olias]

Carlo Rovelli visited this thread earlier, see for example post #42 on page 2.

the thread initially got started around the Fairbairn/Rovelli paper that appeared this year

now Rovelli has a new paper out
http://arxiv.org/gr-qc/0406063
with Simone Speziale and Daniele Oriti.

I thought I'd mention it

BTW the paper cites some people whose work we've discussed in other PF threads
Jan Ambjorn, Etera Livine, Karim Noui,... to name a few

Marcus, have you read this paper yet?..there are some really interesting insights taking foot, and Rovelli, Oriti and Speziale are redefining some pretty longstanding cosmological issue's, which I agree with totally.

 

[selfAdjoint]

It's really a fine piece of work. I am still working on the theory, but these are some exciting results. It's nice to see the Italian and German schools working together, too.

 

[marcus]

Marcus, have you read this paper yet?..there are some really interesting insights taking foot, and Rovelli, Oriti and Speziale...

I've made several unsuccessful attempts. don't have a good understanding
of the things this paper is based on, so i find it hard going

I assume you are referring to gr-qc/0404063 which was the link in your post. It would be great if someone would volunteer some explanation of that paper

 

[marcus]

Chunky makes it into Smolin's standard LQG treatment

chunkymorphisms seemed like a long-shot at the time
(which may explain a bit of their appeal to me)
but they just were included in the latest standard version LQG

smolin
"Invitation to LQG"
http://arxiv.org/hep-th/0408048

see footnote on page 9, citation to Rovelli Fairbairn

this "Invitation" is a bridge paper to physicists in other fields
with possible interest in LQG research----has FAQ and list of open
problems and prospective on observational testing

have to go, must finish this later