David Louapre, at Lyons, another one to watch

[marcus]

http://www.ens-lyon.fr/~dlouapre/

home page has a CV
also a link to some funky music
and a card for French "buzzword bingo"
I am finding as I go along that the newest work in
quantum gravity is being done by virtual children
from my (perhaps too old) perspective

edit: I see that Louapre was born in 1978
The cry of "Bingo" in French is apparently "Foutaise" which sounds
slightly racy to me

even Rovelli, at marseilles, who has the written the book
on current efforts to quantize GR, looks to be
rather young from his photo----35 at most I'd guess---
and he's one of the senior people

Anyway Louapre has come up with interesting ideas
vis-a-vis the "assymptotic 10j" obstacle which Baez
identified one year ago in some papers he and some others wrote circa September 2002
( mentioned a few days ago in TWF #198).

So I will try to get some links to a David Louapre paper or two.
And then as Baez said there will be a conference on spin foams
in Spring 2004 in marseilles and Louapre (does he even have his PhD yet?) is one of the organizers and we will see what he says
there. But in the meantime I will post what I can find in this thread

edit: Here is one from December of last year
http://arxiv.org/abs/gr-qc/0212001
"Diffeomorphisms and spin foam models"

 

[selfAdjoint]

Marcus, I didn't know you were old enough to consider 35 young! As you go along you will find that age becomes meaningless and the 21 year old may have more to say to you than your contemporaries.

 

[marcus]

Originally posted by selfAdjoint
Marcus, I didn't know you were old enough to consider 35 young! As you go along you will find that age becomes meaningless and the 21 year old may have more to say to you than your contemporaries.

Whoah! You took me by surprise. I didnt know anyone would be
reading this thread.

I see where Louapre has an idea vis a vis the "assymptotic 10j"
problem. But it is only partially there and should be completed in a followup paper I have not yet seen.

http://arxiv.org/hep-th/0209134

from the abstract:
"...we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating in agreement with a recent result of Baez et al. We discuss the physical origin of this behavior and a way to modify the Barrett-Crane model in order to cure this disease."

 

[marcus]

A new PhD thesis from Marseilles

this week a new PhD thesis was posted
by Etera Livine (directed by Carlo Rovelli)
http://arxiv.org/gr-qc/0309028

"Boucles et Mousses de Spin en Gravite Quantique"

Livine has already published a number of shorter papers with
Robert Oeckl, Daniele Oriti, and possibly others---I forget.
He sometimes goes by his middle name Richard.

As the epigraph of his thesis, Livine quotes from the Babylonian Talmud:

"It is never advisable for anyone to speculate on these 4 questions:

What is above?
What is below?
What was there before the world?
What will there be after it?

It would have been better for him had he never been born."

In fact I noticed Livine's research several months ago and have
found several of his papers (co-authored with others) of some interest. So I found his thesis in the course of a regular check on
what he and other young European researchers have been posting.

 

[marcus]

the gnome hiding in the low energy limit

I recently exchanged email with Carlo Rovelli and learned that he is in Rome (La Sapienza) this season, rather than at his homebase at the University of the Mediterranean (Marseilles).

Who but Giovanni Amelino-Camelia is at La Sapienza?

This summer, Giovanni A-C posted what I think is a major paper with Smolin. The paper is short, 19 pages, but could have considerable impact. I would guess that Rovelli wants to understand the conclusion and that it may influence a chapter of his draft book or some aspect of his research.

http://arxiv.org/hep-th/0306134
"Quantum Symmetry, the cosmological constant and Planck scale phenomenology"

One often hears that some theories of gravity have difficulty assimilating the case with a positive cosmological constant.
Perhaps this is because of some built-in Poincare invariance! Whether or not this is true, this is what I have seen mentioned from time to time, and it is suggestive of one of the results in this paper. The abstract says:

"We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory, not under the Poincare group, but under a deformation of it parametrized by a dimensional parameter proportional to the Planck mass...
The argument makes use of the fact that the cosmological constant results in the symmetry algebra of quantum gravity being quantum deformed, as a consequence when the limit
l_Planck² Λ--> 0
is taken one finds a deformed Poincare invariance..."

Something interesting is going on here. Some months back in a PF thread I calculated this l_Planck² Λ quantity---the Planck area multiplied by the cosmological constant--- and I recall it came out to be about 1.3E-123. That is very small-----the cosmological constant or "dark energy" density is believed by cosmologists to be non-zero and very important (73 percent of the energy in the universe) but also very small, so that its ratio to the corresponding Planck quantity is
10^-123.
Incredibly, this positive dark energy constant must have the effect of deforming Poincare invariance (by the argument of
Giovanni A-C et al) so that when one looks for the low energy limit under a tree root or large leaf one finds not an ordinary gnome but a deformed ---perhaps hunchback----gnome. A good theory of gravity, therefore, should not have Poincare invariance at its low energy limit but rather should have deformed Poincare invariance.

This paper is also interesting because it relies comparatively more on verbal reasoning and less on equations. What equations it has are on the simpler side----lists of commutation relations for
a couple of κ-Poincare algebras. I must say it piqued my curiosity about this type of algebraic deformity.

 

[marcus]

Stephon Alexander at SLAC Stanford is another one to watch

I already posted about Stephon A, who is in the high energy physics theory group at SLAC. He recently tried his hand at Quantum Gravity and got a nice result. The link I gave earlier is

http://arxiv.org/hep-th/0309045

"Quantum Gravity and Inflation"

Here is a sample from the paragraph of conclusions at the end of that 18-page paper:

"The results of this paper represent a step towards a detailed study of the very early universe beyond the semiclassical approximation, in which quantum gravitational effects are treated in a non-perturbative and background independent manner. For each potential V(φ) and classical slow roll solution u(T) consistent with inflation, we have found a quantum state given by (56) which is an exact solution to the quantum equations of motion, but has a classical limit given by that classical solution. Furthermore we can construct normalizable states which are wavepackets around the initial conditions that generate that classical solution. Thus, inflation is here described in terms of exact quantum states..."

 

[dlouapre]

That's funny because I have to prepare a CV and I tried to take a look at CV's of quantum gravity researchers by typing something like "CV quantum gravity" on google...and I just found this thread talking about my CV on my highly non-updated web page ! I should update that :-)

David

Originally posted by marcus
http://www.ens-lyon.fr/~dlouapre/

home page has a CV
also a link to some funky music
and a card for French "buzzword bingo"
I am finding as I go along that the newest work in
quantum gravity is being done by virtual children
from my (perhaps too old) perspective

 

[dlouapre]

By the way I should say that what we proposed to cure the 10j problem is so far a very "ad hoc" modification and I don't really believe in that anymore...but I've got new ideas on this issue..not yet enough to write a paper on that.

David

Originally posted by marcus
[B}

I see where Louapre has an idea vis a vis the "assymptotic 10j"
problem. But it is only partially there and should be completed in a followup paper I have not yet seen.

http://arxiv.org/hep-th/0209134

from the abstract:
"...we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating in agreement with a recent result of Baez et al. We discuss the physical origin of this behavior and a way to modify the Barrett-Crane model in order to cure this disease." [/B]

 

[marcus]

Originally posted by dlouapre
By the way I should say that what we proposed to cure the 10j problem is so far a very "ad hoc" modification and I don't really believe in that anymore...but I've got new ideas on this issue..not yet enough to write a paper on that.

David

hello David, it is very nice to hear from you

can you give us any idea of what Carlo Rovelli's talk
this Friday about spin foams will cover---any new work
that's likely to form the basis of the talk?

I used the Foutaise card from your website to teach
two French visitors how to play Foutaise, last month.
They had never heard of this game but, having connection
to industry, they understood it very well

 

[dlouapre]

I'm not at the strings/loop meeting but I know that Carlo Rovelli's talk will actually be given by my boss Laurent Freidel. I don't know what's going to be inside the talk because Laurent hadn't finished it when he left for Germany.

However it's going to be a review talk intended for non-expert audience (string people) so don't expect too much fresh news in it, i think...

 

[marcus]

Originally posted by dlouapre
I'm not at the strings/loop meeting but I know that Carlo Rovelli's talk will actually be given by my boss Laurent Freidel. I don't know what's going to be inside the talk because Laurent hadn't finished it when he left for Germany.

However it's going to be a review talk intended for non-expert audience (string people) so don't expect too much fresh news in it, i think...

Thank's for the news David, I will be hoping to hear about
Freidel's talk soon. (after Friday)

best wishes,

marcus

 

[selfAdjoint]

BTW, I just heard from Thiemann, and he's going to give a talk at the meeting by video (he won't be there in body). Marcus we are on the edge of wonders!

 

[marcus]

Originally posted by selfAdjoint
...we are on the edge of wonders!

some changes for sure!

I am happy and at the same time frustrated with the F/L
paper, they say the heart is section 4
I can sort of understand or feel I WILL be able to understand section 2, and section 3 is technical so that one only needs to be able to apply the key things from it to 4
but when I look at 4 I am a bit humbled.
As by the London times sunday cryptic crossword which articulate person should be able to solve but they normally cannot---it is mostly not arcane it is just hard chains of reasoning. besides today was hot

but I do think that F/L paper "spin networks for non-compact..." is important, and likewise Livine's thesis, so if I could just understand them I would feel on the edge of something

I'm glad you are taking a break and will see the fall colors in Wisconsin, Illinois and so on---hope you find trip satisfactory---I could use a break. I think id like to go sailing but I don't have a boat.

keep me posted please if you learn more of the goings on

 

[selfAdjoint]

Well, I've got a couple of days here yet. Why don't we try digging into that section 4 of F/L "Projective..." and share our thoughts here? I want to see how they do Lorentz boosts!

 

[dlouapre]

That's a well written paper. Here are some guidelines for section 4 :

The key part to understand is 4.1.1
It contains the definition

4.1.2 is generalization to many Cartan and is formally the same if you understand Weyl integration formula.

4.2 is generalisation, no too hard since (4.29) shows that the h petals case is not really more difficult than 2 petals case.

4.3 mixes that with the flower construction, the key step being the invariance under the change of maximal tree which is proven by showing that two trees can always been related by a sequence of 'moves' and that the gauge fixing procedure gives the same results under the moves.

If you get 4.1.1 the remaining part should follow, maybe you'll have to think a little more for 4.3 and the proof of invariance.

David

Originally posted by selfAdjoint
Well, I've got a couple of days here yet. Why don't we try digging into that section 4 of F/L "Projective..." and share our thoughts here? I want to see how they do Lorentz boosts!

 

[marcus]

In case anyone is just joining us the comments here refer to
http://arxiv.org/hep-th/0205268
"Spin Networks for Non-Compact Groups". Section 4.1.1 (that is, 4.1 part 1) begins near bottom of page 13 and is called
"1. Case of a unique Cartan subgroup H"

Section 4.1.2 (that is, 4.1 part 2) begins on page 16 and is called
"2. The case of many Cartan subgroups"

Originally posted by dlouapre
That's a well written paper. Here are some guidelines for section 4 :

The key part to understand is 4.1.1
It contains the definition

4.1.2 is generalization to many Cartan and is formally the same if you understand Weyl integration formula.

4.2 is generalisation, no too hard since (4.29) shows that the h petals case is not really more difficult than 2 petals case.

4.3 mixes that with the flower construction, the key step being the invariance under the change of maximal tree which is proven by showing that two trees can always been related by a sequence of 'moves' and that the gauge fixing procedure gives the same results under the moves.

If you get 4.1.1 the remaining part should follow, maybe you'll have to think a little more for 4.3 and the proof of invariance.

David

In fact it was just at 4.1 part 1, which David calls the key part to understand (containing the definition in the simplest case) that I was having difficulty understanding earlier (essentially page 14). Just got back home and will make another attempt at it.

 

[marcus]

I need some help understanding the case where the group is SL(2,C)

then, referring to page 9, there is only one Cartan subgroup
I am not familiar with Cartan subgroups but I tentatively imagine that in this case things might reduce to something quite understandable and elementary.

Hopefully someone can help me out here. Perhaps if G is just SL(2,C) then, in the notation of the Freidel/Livine paper, the cartan subgroup H is, say, the diagonal matrices with determinant unity.

Corresponding to that H, the Weyl group is N(H)/H where N(H) the normalizer of H

and I think if H is diagonal matrices then the normalizer consists of H AND the counterdiagonals (the minor as opposed to major diagonal) always with det = 1.

so then the Weyl group is looking to me like Z₂, kind of like a boolean toggleswitch which decides to flip the main to the minor and the minor back to the main

to my embarrassment I never did study about Cartan and Weyl subgroups, but in this one example they seem to be nice ideas

if we can get this one case, then section 4 of that paper will boil down to section 4.1 alone and we can see how to construct the measure

 

[marcus]

...so then the Weyl group is looking to me like Z₂, kind of like a boolean toggleswitch which decides to flip the main to the minor and the minor back to the main

to my embarrassment I never did study about Cartan and Weyl subgroups, but in this one example they seem to be nice ideas

if we can get this one case, then section 4 of that paper will boil down to section 4.1 alone and we can see how to construct the measure

Since cartan and weyl groups are new to me i am flying blind, or relying on guesses---presumably all or partly wrong in this first attempt

I would suppose that the cartan subgroup of SL(2,C) is NOT a normal subgroup
and yet on page 9 there is an integral over G/H
this G/H, I should imagine, is not a group(!) if H is not normal
I should picture it as a bunch of cosets, or as a bunch of equivalence classes

a kind of easy trick (equation 3.6) is used to define a measure on it

so already I'm curious to know what G/H looks like
perhaps it is non-compact!

but to visualize G/H I must be more certain as to what the cartan subgroup H is. I was thinking (main) diagonal matrices with entries (z, 1/z) on diagonal where z is any complex number. But maybe this is not right?

 

[marcus]

page 9 has a defintion we need later
G₁, it says, consists of elements of G which can be conjugated to a Cartan subgroup

the simple case I have in mind is SL(2,C) where there is just one cartan subgroup---diagonal matrices I'm presuming for sake of argument. so G₁ would be "diagonalizable" matrices

it also says they're going to call those element "regular", so G₁ is the regular elements of G

it also says that G₁ consists of elements x for which Adx is diagonalizable. I am not sure what it means for Ad x, the adjoint mapping, to be diagonalizable.

it also says that G₁ is almost the whole group G, that is its complement has haar measure zero.

well, courage, things look to be in a pretty desperate pass, but dlouapre says this is a well-written paper (the F/L "Spin Networks for Non-Compact Groups") and it looks that way to several others including me, and if we just restrict attention to the group we need namely SL(2,C) maybe we can understand some of this paper and be better off for having tried.

We have to know what G₁ is because the very first thing they do in section 4.1.1, the heart of the paper, is define an injection G₁ --> A₂

 

[marcus]

that reminds me, what is A₂

well on page 12 they define it as G₂/Ad(G)

and say it is a geometric quotient of same dimension as the group G (this is in the "rank one" case which I think we are in)
and
what G₂ is might be understandable as the set of pairs in G x G for which a certain combination that one is going to need to diagonalize is in fact "regular" or "G₁"
basically G₂ is equal to G x G except for measure zero and is a convenience set that has some nasty pairs removed so I will think of it as just G x G

so this key thing A₂ is essentially (G x G)/Ad(G)

and this mapping they define on page 13 (in section 4.1.1 the only section I want to really understand for sure) is a map
j : G₁ --> GxG/Ad(G)

this map j (which depends on choosing a section s(x) but then turns out the measure doesn't depend on the choice, the old story)
this map j is how they define the friggin measure

so if I can just understand this map j
of equation (4.1) on page 13

 

[marcus]

AH! the set G₁, they said earlier, consists of things that can be conjugated to a (the unique in our case) cartan subgroup

that is why in equation (4.1) when they define the map j
they can write an element of G₁ as xhx^-1
where h is in the cartan subgroup H

so then they have a grip on this element g of G₁
they have information h, and x, about it
and they have chosen a section s: G/H --> G
and x is in G/H ( a little abuse of notation, x is a representative of an equivalence class, but only just a whiff of abuse)

and so the section defines s(x) in G
and we have a pair (h, s(x)) in H x G
and we can take its ORBIT by moving that point around
wherever it can go by the adjoint action of the whole group
and the orbit is written
Ad(G).(h, s(x))

Now j is supposed to map G₁ into this set G x G/Ad(G)
(with a measure zero set of bad points removed)
and it looks like now with have a pair (h, s(x))
and the mapping is supposed to go into an orbit space or space of equivalence classes mod Ad(G), so heck NO PROBLEM it looks like we have our map!

that was not as bad as I expected, but now we are at the top paragraph of page 14, which is the tough place of the whole paper. they start talking about "this is a gauge fixing but it only partially fixes the gauge" OK OK I have the map j, now I want to see the measure---the whole paper is about getting this measure in the non-compact case, in the SL(2, C) case. Let us try to get it.

 

[dlouapre]

Think about the SU(2) case first and everything will become clear (it's not because its compact that the method doesn't apply)

So take the SU(2) group elements in terms of Euler angles.

g(phi,theta,psi)=h(phi) a(theta) h(psi)

where h(phi) are the 2x2 matrices diagonal with e^{i phi},e^{-i phi} on the diag.

a(theta) are the 2x2 matrix

[ cos theta -sin theta ]
[ sin theta cos theta ]So the cartan subgroup H is just given by the elements h(phi), and its easy to see that the elements in the coset G/H are just the elements

x(phi,theta)=h(phi) a(theta)

The F/L measure tells you that if you want to integrate f(g1,g2) which is AdG invariant, you should integrate it like that : take g1 in H only and g2 in G/H only.

You can play the game in SU(2) and integrate
f(h(phi),h(psi) a(theta)) over phi,psi and theta.David

 

[marcus]

WHOAH! It's not so hard after all!

you have the map j
so if you want to integrate a function you just pull it back by j
this is what equation (4.3) says to do
I don't quite get it yet but there is hope

I suspect that A₂ is important because it is
the space of graph-based connections for a simple kind of graph
so we have a measure on a space of connectons
and will just have to add more petals

so we want to integrate functions on A₂
and equation 4.3 says to pull them back to G₁
and use haar measure.

this is dangerously iffy, but maybe I am beginning to understand what is happening in this section of the paper

----------
hello David! I did not see your post until just now.
I will read what you say about SU(2) as soon as I get back
to the computer. My wife would appreciate it if I would shave
and get dressed as I am still in pyjamas and it is after 9AM!

 

[selfAdjoint]

O'Raifeartaigh says "For the Lie algebras of the classical groups the Cartan algebra is simply the algebra of all diagonal matrices compatible with the group conditions (unimodular, orthogonal, symplectic)." So in this general case H = the diagonal 2X2 matrices.

Then the Cartan subgroup is the centralizer of those; a quick check showed me that any 2X2 matrix that commutes with a diagonal one is diagonal itself. So H is the diagonal matrices.

But is it normal? We have to get the set of matrices N such that n^-1hn is in H, for all h in H. So if we take a general (a b, c d) matrix its inverse is (d -b, -c a)/Δ, and doing the multiplication gives bd = 0 and ac = 0, so b = 0 or d = 0 and a = 0 or c = 0. For Δ not zero, we can only have the cases a=0, d=0 and b=0,c =0, giving (0 b,c 0) and (a 0, 0 d), and as you say, then N(H)/H ~ Z₂.

----------edit----------
Hah, looks like while I was scribbling I fell behind the thread. Let me read Dvid's post and we'll be in synch.

 

[selfAdjoint]

Originally posted by marcus

I suspect that A₂ is important because it is
the space of graph-based connections for a simple kind of graph
so we have a measure on a space of connectons
and will just have to add more petals

I think A₂ has two avatars in this paper. One, it's the space of gauge invariant connections on the two petaled flower ( which is itself the quotient of a simple graph by its maximal tree ) and two, it's this factor group. Ultimately we will get to (tensor product of G over edges) modulo (tensor product of restricted group over vertices), and that will be the measure space the cylindrical functions are defined on.

 

[marcus]

hi sA,
I've been reading in chapter 8 of the thesis, pages 99-102 and thereabouts.
he is creating a bridge between the canonical loop gravity we are familiar with (SU(2) Ashtekar, Thiemann and the rest) and spin foams, you and I talked about this earlier I think. it is fascinating to watch the bridge being constructed

Am getting a feel for this scaffolding vectorfield c

in chapter 8 he seems to get a version of the theory which is intermediate between canonical LQG and spinfoams so that he can go either way----but so far I haven't begun to look at how he gets to spin foams, only the derivation of usual LQG

looking forward to resumption of conversation about this on your return next week

so far I have no reports from AEI conf.

 

[selfAdjoint]

so far I have no reports from AEI conf.

Me neither. Thiemann promised to send me his talk (which was not on the schedule), but I don't know if it will come by email or snail.

Sounds fascinating about chapter 8. There's a lot of sniffiness over on s.p.r about LQG does not support Lorentz transformations and I wanted to post, "Hey, I know about some covariant QG, want to see?" But I didn't. Leaving in about an hour, as soon as my daughter gets back from work.