Loop-and-allied QG bibliography

[Janitor]

All I can ever remember seeing at J.B.'s website is QG and category theory. Is he now down to just category theory?

 

[marcus]

Many of the QG pioneers like Ashtekar, Lewandowski, Baez are not publishing much and there is a new crop (many of whom were unknown in the Nineties.)

Baez has not published in QG for several years, or only negligibly.
Ashtekar likewise. But both play an important role. Ashtekar is a big presence at conferences. Baez will be a principle figure at the Marseille QG conference in May and the Dublin conference in July.

I guess the people who started up LQG in the 1990s are already
over 40, maybe pushing 50. Ashtekar must be over 50. So with some exceptions it really seems to be the next wave of young LQGists that is making the field progress

maybe the term is "mathopause"----it gets mathematicians
you could have direct knowledge yourself so why elaborate

 

[Janitor]

Thanks for the info, Marcus.

Yeah, I guess I'm at that age. Of course, I never had the right stuff in the first place!

 

[marcus]

the great John Baez burnout

Originally posted by Janitor
Yeah, I guess I'm at that age...

argh! bummer! confession is the pits.

I actually think Baez might blossom again, just in a different field. he is a remarkable guy.
and if he can maybe there is hope for the rest of us.

meanwhile there are up-and-coming people in LQG to watch
here are a few names off the top of my head in no
particular order
Etera Livine
Laurent Freidel
Phillipe Roche
Martin Bojowald
Karim Noui
Hanno Sahlmann
Velhinho
Kowalski-Glikman

 

[selfAdjoint]

My thesis advisor, Ed Fadell, published important research in the later 1990's. He was pushing 40 when I knew him in the early 1960's, so probably he was 70 when he did that. Don't ever count anybody out.

 

[marcus]

My thesis advisor, Ed Fadell, published important research in the later 1990's. He was pushing 40 when I knew him in the early 1960's, so probably he was 70 when he did that. Don't ever count anybody out.

Algebraic topology, impressive, maybe abstract algebra too?
Had a student by the name of Bob Brown whom I may have met but am not sure (he did abstract algebra IIRC, was teaching galois theory)

just happened on this:
E. Fadell, Homotopy groups of configuration spaces and the string problem of Dirac, Duke Math.J. 29 (1962), 231-242.

Edward Fadell apparently had several topnotch students which is another
dimension---the vitality that goes into that, as well as research. It is possible you made a real good choice of advisor
genes, character
we should all have it whatever it is that never stops
Are grand old men more the norm in physics?
Hans Bethe
did you ever look at the "mathematical geneology" website
it is like the Begats in the bible
I looked up Marc Rieffel not long ago
George Mackey advised Rieffel
and so and so advised Mackey and...

back to Birkhoff at Harvard around 1905 if I remember right

 

[selfAdjoint]

You met Bob Brown?! He and I studied together - in fact I was a fixture at his and his wife Brenda's apartment, since I had no significant other of my own then. Bob's had a standout career at UCLA.

 

[marcus]

You met Bob Brown?! He and I studied together - in fact I was a fixture at his and his wife Brenda's apartment, since I had no significant other of my own then. Bob's had a standout career at UCLA.

Im not sure it was the same Bob Brown
algebraist (I formed a high opinion of him as a teacher and person)
could be the same, I'll write you a PM later

 

[marcus]

this just out
http://arxiv.org./abs/gr-qc/0403106

"Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity"
Martin Bojowald, James E. Lidsey, David J. Mulryne, Parampreet Singh, Reza Tavakol
15 pages, 8 figures

"Loop quantum gravity (LQG) or quantum geometry is
at present the main background independent and non–
perturbative candidate for a quantum theory of gravity
(see for example [1, 2]). Key successes of this approach
have been the prediction of discrete spectra for geometrical
operators [3], the existence of well defined operators
for the matter Hamiltonians which provides a cure for
the ultraviolet divergences [4], and the derivation of the
Bekenstein–Hawking entropy formula [5].

Given that LQG effects are likely to have important
consequences in high energy and high curvature regimes,
early universe cosmology provides a natural environment
to test these new features...

From the loop quantum cosmology (LQC) perspective,
the evolution of the universe is comprised of the three distinct
phases. Initially, there is a truly discrete quantum
phase which is described by a difference equation [9, 10].
A key consequence of this discretization is the removal
of the initial singularity [9]. As its volume increases,
the universe enters an intermediate semi–classical phase
in which the evolution equations take a continuous form
but include modifications due to non–perturbative quantization
effects [12]. Finally, there is the classical phase
in which the usual continuous ODE/PDE cosmological
equations are recovered and quantum effects vanish..."

 

[marcus]

also just out, Clifford Will's paper, could be the same paper he gave last week at Ulm to the German Physical Society

http://arxiv.org./abs/gr-qc/0403100

"Testing Alternative Theories of Gravity Using LISA"

-----quote from abstract-------
We investigate the possible bounds which could be placed on alternative
theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter ω of scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton λ_g in hypothetical massive graviton theories.

In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 103M⊙ black hole in the Virgo Cluster,
in a two-year integration, we find a lower bound ω > 3 × 10^5. For lower-mass black holes, the bound could be as large as 2 × 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 × 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7M⊙. For the
highest-mass systems (10^7M⊙), the bound is proportional to (LISA arm length)1/2 and to (LISA acceleration noise)^−1/2. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.
---------end quote-------

 

[meteor]

Initially, there is a truly discrete quantum
phase which is described by a difference equation [9, 10].
A key consequence of this discretization is the removal
of the initial singularity [9]. As its volume increases,
the universe enters an intermediate semi–classical phase
in which the evolution equations take a continuous form
but include modifications due to non–perturbative quantization
effects [12].

Is there any paper that can says when exactly in time the evolution of the universe change to be described by a difference equation to be described by differential equations?

 

[marcus]

Is there any paper that can says when exactly in time the evolution of the universe change to be described by a difference equation to be described by differential equations?

IIRC Ashtekar's paper "Quantum Geometry in Action: Big Bang and Black Holes"
gives an estimate of several hundred steps (of the difference equation) to converge to the semi-classical model

it is the usual sort of limiting process
the quantum regime converges to the semiclassical (after a very short period on the order of 100 Planck time units)
and the semiclassical converges thereafter more gradually to
the ordinary or partial differential equation model
but as with other kinds of convergence one cannot say with precision the exact moment when
the discrete model stops being appropriate and the semiclassical model
begins to apply
there is a transition period when both are giving approximately the same answer

So what one needs is a rough order of magnitude idea of when the transition between models happens. If it is not in that Ashtekar paper then I must be thinking of one by Ashtekar, Bojowald, Lewandowski called
"Mathematical Structure of Loop Quantum Cosmology"

I will try to get a link and page reference for the several hundred Planck time units or DiffEq timesteps---it's in one or the other or both papers. May be other places as well so someone else could come up with yet another link.

------------LONG LAPSE OF TIME-----
I forgot to get the references, however the one I mentioned first has something.
See page 10 of gr-qc/0202008, last paragraph of section 3.1 "Big Bang".
Ashtekar says there that the semiclassical model (Wheeler-DeWitt) is recovered when the scale of the universe is a few hundred Planck lengths. that is, very soon.
Also next to last paragraph on page 8.
I would like to find a more recent and more precise paper, in answer to your question. At the moment I don't have one. Perhaps someone else out there does.

 

[marcus]

"3.3 Chern-Simons perturbation theory.
Setting
\frac{3}{4} = \frac{2}{3}
our Lagrangian becomes the Chern-Simons-functional..."

there is a mathematician named Dror Bar-Natan
on page 19 of this paper
q-alg/9702009
"The Fundamental Theorem of Vassiliev Invariants"
he claims to prove something
by setting 3/4 equal to 2/3.

His paper is about the "Fundamental Theorem of Vassiliev Invariants"
and it is divided into four sections with four different ways of proving
the fundamental theory and at the end of each section he has
a concluding paragraph entitled
"Why are we not happy?"

This shows a philosophical concern with the problem of human happiness.
Also he proves the theorem by algebra, by physics (the oldest way, already almost 10 years old), by geometry, by topology. and he finds something always unsatisfying or wrong. in the middle of the proof by physics he says
"This is of course silly."

Dror Bar-Natan has an unusual expository style. Or at least I hope that it is unusual.

BTW he calls the topological method "combinatorial-topological" because doubtless he thinks of combinatorics and topology as very close neighbors or almost joined at the hip

He cites V.I.Arnold a russian mathematician. Fairbairn and Rovelli also cited a book by V.I. Arnold. It would be possible to suspect that something is going on with knot theory and Vassiliev invariants. the quirky Bar-Natan tone of voice even encourages this suspicion.

Perhaps it will be necessary to classify knots-with-nodes and I cannot at the moment visualize how this would be done.

I will get the LQG paper by Gambini and Pullin that cites this Bar-Nathan.
Nonunitary gave this link in another thread.

------quote from nonunitary post in "chunkymorphism" thread---
...As far as I know the first paper about the invariants was

gr-qc/9803018

but you are right about the chunkymorphisms. The are a new invention of Rovelli. I haven't read the paper so I can not comment.
-----endquote----

the Gambini/Pullin paper
http://arxiv.org/gr-qc/9803018
is called
"Vassiliev invariants: a new framework for quantum gravity"

 

[selfAdjoint]

How do you get to those q_alg papers in the arxiv? I have been trying every trick in the book for half an hour now and nothing! Click on mathematics and get, but can't ge q-alg or QA. Click on 1997 and search, nothing.

 

[marcus]

How do you get to those q_alg papers in the arxiv? I have been trying every trick in the book for half an hour now and nothing! Click on mathematics and get, but can't ge q-alg or QA. Click on 1997 and search, nothing.

only have a minute to reply but try
http://arxiv.org/PS_cache/q-alg/pdf/9702/9702009.pdf

will get back in a few minutes and check that this works

Im back.
this should get the abstract:
http://arxiv.org/q-alg/9702009

now I understand. the problem is to use the search engine
to find a paper like this one, but hopefully more recent
------------------

go to arxiv
don't click on search immediately
because right beside the button that says "search" there is
a menu box where you can select "math"

select "math" and then click on "search"

you then get a form where you can type in Author and Keyword
I typed in Bar-Natan and knot
and got many QA papers including this sample

3. math.QA/0201043 [abs, ps, pdf, other] :
Title: On Khovanov's categorification of the Jones polynomial
Authors: Dror Bar-Natan
Comments: Published by Algebraic and Geometric Topology at this http URL, 34 pages with many figures, source contains associated program and data file
Subj-class: Quantum Algebra; Geometric Topology
MSC-class: 57M25
Journal-ref: Algebraic and Geometric Topology 2 (2002) 337-370

 

[selfAdjoint]

Thanks. Using your hint, I fooled around and found it with"Vassiliev invariants" which is what I was interested in anyway. Bar-Natan's motive for "why are we not happy" is perfectly clear; he wants to impose on his students a careful understanding of what it means to have a "proved theorem" which you can use to prove other things, and what it does NOT mean - which is the status of what he calls the fundamental theorem of Vassiliev invariants.

 

[marcus]

Hi selfAdjoint, I concur with your description of Bar-Natan's
serious and commendable motive but I also delight immoderately in
his sense of humor
which he uses to the hilt in implementing his serious idea

thanks to nonunitary for this, I never would have seen the paper if
he had not referred to that one by Gambini and Pullin about LQG and
the Vassiliev invariants

you know diff manifolds are in a deep sense just gussied up Rⁿ
and it just shows you what an enormously rich thing Euclidean space is
that you can have all these different variations on that theme
the theme of the continuum
the theme of the coordinate patch and the metric
all fundamentally Rⁿ at the root

can knots and networks be comparably rich
why is there all this interest in them just now
well this is not purely a rhetorical question although it
sounds like it, I was actually wondering, but not expecting to
be able to get an answer

it was clever of you to study algebraic topology in grad school
maybe it will be useful after lo these many years

 

[marcus]

You might be interested to have a look at Frieder Lenz's
lecture notes on
"Topological concepts in gauge theories"

http://arxiv.org./hep-th/0403286

the whole thing is 83 pages

http://arxiv.org./PS_cache/hep-th/pdf/0403/0403286.pdf

They just came out.
he has a good historical sense and begins with a story about something that happened in 1833 involving Carl Gauss and a magnetic monopole :-)

these notes strike me as student-friendly
by someone who is considerate and puts in some nice pictures
Getting ready for a Brahms Req rehearsal tonite.
Up to you to decide if Frieder Lenz's notes are good or not and for what.

 

[selfAdjoint]

Thanks for the links, Marcus.

You know, reading Bar Natan's account of the topological proof of his "fundamental theorem" and its defects, I couldn't help thinking here's a natural arena for spectral sequences. That's only because I'm reading A User's Guide to Spectral Sequences at the same time, but seriously there are his filtered graded algebra and all - by a theorem, there is guaranteed to be a spectral sequence with the 1-page E^{p,q}_1 isomorphic to the homology of the algebra. But that's no good unless you can compute the limiting page E^{p,q}_{\infty}. The differentials of the sequence encode non trivial information about the algebra. I can't believe somebody hasn't tried this.

 

[marcus]

Bolen, Bombelli, Corichi
http://arxiv.org./abs/gr-qc/0404004
"Semiclassical States in Quantum Cosmology: Bianchi I Coherent States"

"We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical states in the kinematical Hilbert space and corresponding ones in the physical Hilbert space, which we construct here using the group averaging technique. We find that it is possible to construct good semiclassical physical states by such a procedure in this model; we also discuss the sense in which the original kinematical states may be a good approximation to the physical ones, and the situations in which this is the case. In addition, these models can be deparametrized in a natural way, and we study the effect of time evolution on an "intrinsic" coherent state in the reduced phase space, in order to estimate the time for this state to spread significantly."

 

[john baez]

the great John Baez burnout

Baez has not published in QG for several years, or only negligibly.

Well, I don't think my paper with Christensen and Egan on asymptotics of 10j symbols was negligible - it contained the results of literally billions of calculations, and it was the first detailed analysis of a spin foam model of quantum gravity. And that was back in August of 2002, which isn't several years yet, just a couple! "Several" means at least 3!

But, you're right in perceiving that I'm mainly interested in other things
these days.

I found out about this thread from Carlo Rovelli, who sent me an email teasing me about it. I couldn't resist replying to an article entitled "the great John Baez burnout"! I'll take it as a compliment, since it suggests there was a flame flickering there for a while.

Here's how I replied to Rovelli's email:

Dear Carlo -

Hi! I hadn't seen these... thanks. It's pretty funny.
You know you're getting old when you start getting emails
with subject headers like this.

I am in fact rather fed up with quantum gravity. One reason is that
nobody knows a spin foam model that approximates GR in the classical
limit, and I don't see how to get one, despite a lot of work. But
there's another, equally important *positive* reason: these days, work
on n-categories is really revolutionizing mathematics! The subject
is packed with incredible suprises; it goes all the way down to
the foundations of how we think, and there are huge wide-open fields
of fruit ripe for the picking. I can't help but wanting to spend
my time doing this: it's as cool almost as quantum gravity, but I *know*
it will work.

But I might switch back to quantum gravity if and when spin foam
models seem to start working... because I really love the *physical*
universe, and the most mysterious and exciting aspect of math
to me is how it let's us understand the physical universe.

It will be fun to see everyone in Marseilles and see what their
mood is. Probably rather different from mine!


jb

Just so nobody gets the wrong idea: while I'm tired of trying to find a spin foam model with something like GR as its classical limit, I don't see any reason this should be impossible. Christensen, Egan and I just looked at a few versions of the Barrett-Crane model, and we didn't even succeed in ruling those out, just showing that they were far stranger than anyone expected.

I'm even *more* pessimistic about string theory and M-theory - otherwise I might switch to that.

But really, what got me off quantum gravity was the knowledge that I won't live forever. I have a choice of working on quantum gravity, where nobody knows for sure what's right and what's not, and working on mathematics, where I'm *sure* what I'm doing is right. I spent about a decade working on the former; now I want to do more of the latter.

maybe the term is "mathopause"----it gets mathematicians.

Actually, the idea that mathematicians burn out early is a bit of a myth. Sure, some of them *die* early, like Abel and Galois and Riemann. But the ones who keep living often keep doing good stuff - although lots of them get tired of publishing and spend more time just thinking and talking to people, because it's easier and more fun. For example, take Dennis Sullivan, or Erdos (who got other people to do the writing).

In case anyone is interested, I have a new paper called "Quantum Quandaries: A Category-Theoretic Perspective", in which I argue that a lot of the puzzling things about quantum mechanics will become less puzzling when it becomes part of a theory of quantum gravity, because the category of Hilbert spaces is a lot like a category where the morphisms are spacetimes:

http://math.ucr.edu/home/baez/quantum.ps

This will appear in a volume edited by Steven French, Dean Rickles and Juha Saatsi, probably to be entitled "Structural Foundations of Quantum Gravity".

So, I'm not *completely* fed up with quantum gravity.

I'm also working a lot on the foundations of quantum theory:

http://math.ucr.edu/home/baez/qg-fall2003/
http://math.ucr.edu/home/baez/qg-winter2004/
http://math.ucr.edu/home/baez/qg-spring2004/

So, please don't count me out yet!

But, it's true that there's a nice new crop of people working on loop quantum gravity and spin foam models.

 

[jeff]

I won't live forever

Do you have the proof for that?

 

[marcus]

Background Independent Quantum Gravity---survey paper

http://arxiv.org./abs/gr-qc/0404018

Background Independent Quantum Gravity: a Status Report

125 pages

Ashtekar and Lewandowski

 

[cragwolf]

Just call me a Baez fanboy. I have spent countless hours at his website undergoing significant neural rewiring. Because of him I've been inspired to learn mathematics (I mean really learn it, beyond the "mathematical methods for physics" course I took way back in my undergraduate years). Baez is on the cutting edge of physics and mathematics, but he kindly and humbly devotes some of his time to helping us lesser beings learn something about the wonders of these subjects. His website is a pedagogical paradise.

 

[marcus]

well said!

 

[meteor]

"Flat spacetime vacuum in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0404021

Authors: A. Mikovic
Comments: 20 pages, 6 figures

"We construct a state in the loop quantum gravity theory with zero cosmological constant, which should correspond to the flat spacetime vacuum solution. This is done by defining the loop transform coefficients of a flat connection wavefunction in the holomorphic representation which satisfies all the constraints of quantum General Relativity and it is peaked around the flat space triads. The loop transform coefficients are defined as spin foam state sum invariants of the spin networks embedded in the spatial manifold for the SU(2) quantum group. We also obtain an expression for the vacuum wavefunction in the triad represntation, by defining the corresponding spin networks functional integrals as SU(2) quantum group state sums"

Looking at the text, he mentions something called "spin network invariants". Never heard of this before (though I'm familiar with things like knot invariants or manifold invariants)

 

[john baez]

spin network invariants

Looking at the text, he mentions something called "spin network invariants". Never heard of this before (though I'm familiar with things like knot invariants or manifold invariants)

A spin network invariant is a function that assigns a complex number to each spin network embedded in space, where the number doesn't change when you apply a diffeomorphism of space to your spin network. (Here "space" is some 3-dimensional manifold.)

In loop quantum gravity, quantum states are commonly taken to be spin network invariants. You can think of such a state as a big fat linear combination of spin networks, where the coefficients are the aforementioned complex numbers.

If you attach a spin 0, 1/2, 1,... to a knot, you get a spin network of a specially simple kind. So, any spin network invariant gives an infinite sequence of knot invariants. But it has more information.

 

[selfAdjoint]

By the way Dr. Baez, I have printed of and am studying your new Quantum Quandries paper.. How neat! From a sufficiently high perspective, quantum physics and general relativity are more like each other than either of them is like set theory. I am always glad to see set theory marginalized, because of my prejudice for Tarski's theorem and the BSS-machine results.

 

[Janitor]

I've pretty much decided that there isn't a Santa Claus, but is there really a John Baez?

 

[meteor]

The Bianchi IX model in Loop Quantum Cosmology
Authors: Martin Bojowald, Ghanashyam Date, Golam Mortuza Hossain
Comments: 41 pages, 3 figures, revtex4
Report-no: IMSc/2004/04/16, AEI-2004-028

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities
http://arxiv.org/abs/gr-qc/0404039