Loop-and-allied QG bibliography

[Ambitwistor]

(Oops, that should be "L-C connections", i.e. "Levi-Civita".)

 

[Ambitwistor]

Example: Yang-Mills gauge theories are geometric theories, even though they're not Riemannian geometries.

The gauge field A (e.g., the the scalar and vector electromagnetic potentials, together forming the 4-potential) is given by a connection, and the field strength tensor F (e.g., the electric and magnetic fields, together forming the Faraday tensor) is the curvature of that connection.

So, in addition to gravity, the fields of the Standard Model (electromagnetic, weak, strong) are also given by geometric theories, but it's not the Riemannian spacetime geometry of general relativity. The Ashtekar variables exploit this similarity by recasting general relativity in a form more similar to the geometry of other gauge theories. You can also go the other way, and try to recast the gauge theories in a form more similar to the geometry of conventional general relativity, in which case you get Kaluza-Klein theory.

 

[marcus]

Originally posted by Ambitwistor
Only a Levi-Civita connection specifies a Riemannian geometry, because only L-V connections are compatible with metrics. But starting at least with Klein, and certainly since Cartan, the notion of "geometry" has been expanded to include geometries other than Riemann's. You can think of a connections as giving a generalized kind of geometry, a special case of which are the Riemannian (metric) geometries.

At the start of the thread here I was hoping to find a way of presenting an intuitive picture of loop gravity.

Now I'm recalling the explanatory job Baez did on a variety of formalisms for GR---Palatini, Ashtekar-Sen, Barbero variation---I believe it was in TWF with references to hardcopy (the book by Ashtekar, which I have not read having been spoiled by the internet). Now I am thinking that either it is impossible to do what I had in mind. Or Baez will do it and put it on his website one of these days. Or one of the others (of several talented writers in loop gravity.) Or else...the way to go is to start with what you just said "You can think of a connections as giving a generalized kind of geometry, " and (possibly by means of dervish-like handwaving) OMIT the construction of the new GR variables but just take as given that a manifold has a space of all possible connections which reflects all its possible geometries and just go from there. *Takes a deep breath*

Was delighted by one of the other poster's (Gale's) idea of a wickedly clever third grader---which you elucidated by classical anecdote--and am wondering if that approach to quantum gravity would fly with such a third grader.

 

[eigenguy]

Originally posted by marcus
At the start of the thread here I was hoping to find a way of presenting an intuitive picture of loop gravity.

I am studying the following paper

http://arxiv.org/abs/gr-qc/0207106

Abstract: A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. Maxwell fields will be discussed in the second paper of this series which further develops the program and provides details.

Here's an excerpt:

"We will begin with the usual Weyl algebra generated by the exponentiated position and momentum operators. The standard Schrodinger representation of this algebra will play the role of the Fock representation of low energy quantum field theories and we will construct a new, unitarily inequivalent representation called the polymer particle representation in which states are mathematically analogous to the polymer-like excitations of quantum geometry. The mathematical structure of this representation mimics various features of quantum geometry quite well; in particular there are clear analogs of holonomies of connections and fluxes of electric fields, non-existence of connection operators, fundamental discreteness, spin networks, and the spaces Cyl and Cyl*. At the basic mathematical level, the two descriptions are quite distinct and, indeed, appear to be disparate. Yet, we will show that states in the standard Schrodinger Hilbert space define elements of the analog of Cyl*. As in quantum geometry, the polymer particle Cyl* does not admit a natural inner product. Nonetheless we can extract the relevant physics from elements of Cyl* by examining their shadows, which belong to the polymer particle Hilbert space HPoly. This physics is indistinguishable from that contained in Schrodinger quantum mechanics in its domain of applicability.

These results will show that, in principle, one could adopt the viewpoint that the polymer particle representation is the `fundamental one'|it incorporates the underlying discreteness of spatial geometry|and the standard Schrodinger representation corresponds only to the 'coarse-grained' sector of the fundamental theory in the continuum approximation. Indeed, this viewpoint is viable from a purely mathematical physics perspective, i.e., if the only limitation of Schrodinger quantum mechanics were its failure to take into account the discrete nature of the Riemannian geometry. In the real world, however, the corrections to non-relativistic quantum mechanics due to special relativity and quantum eld theoretic effects largely overwhelm the quantum geometry e ects, whence the above viewpoint is not physically tenable. Nonetheless, the results for this toy model illustrate why an analogous viewpoint can be viable in the full theory: Although the standard, low energy quantum field theory seems disparate from quantum geometry, it can arise, in a systematic way, as a suitable semi-classical sector of loop quantum gravity."

 

[meteor]

I'm trying to learn what the different spaces of LQG are useful for,for example I more or less know the utility of the Hilbert space, the configuration space and the phase space. But, what's the utility of the state space?
My resumee:
In LQG the two basic variables are a connection and a densitized triad field(sometimes called electric field). The connections are functions defined in the configuration space of the theory, and each connection represents a quantum state of spacetime.This configuration space is a vector space of functions
The connection and the densitized triad field form a canonical pair in the phase space of LQG, that is a infinite dimensional space
The Hilbert space of the theory is constructed of the connections defined in the configuration space. Spin network states (previously were used loop states) form the basis of this Hilbert space.
Now, is this Hilbert space the unique Hilbert space of the theory? I've read that there's something called "kinematical Hilbert space", and othe thing called "diffeomorphism invariant Hilbert space". They both refer to the same thing?
Would be good if you could clarify this: It's true that actually the complex SU(2) connection of Ashtekar is not used in LQG, but is used the real SO(3) connection introduced by Barbero?

 

[Ambitwistor]

Originally posted by meteor

In LQG the two basic variables are a connection and a densitized triad field(sometimes called electric field). The connections are functions defined in the configuration space of the theory, and each connection represents a quantum state of spacetime.

Each connection (modulo an SU(2) or SO(3) gauge transformation) represents a classical state of space, not a quantum state of spacetime. (Well, not even that: it only represents space once you impose the constraints.) We haven't quantized yet.

Spin network states (previously were used loop states) form the basis of this Hilbert space. Now, is this Hilbert space the unique Hilbert space of the theory? I've read that there's something called "kinematical Hilbert space", and othe thing called "diffeomorphism invariant Hilbert space". They both refer to the same thing?

No. The kinematical Hilbert space is L^2(A/G), i.e., the (complex) Lebesgue square-integrable functions over the space of connections modulo gauge transformations. It's like saying that the configuration space of a particle is R^3 (all of space), and then saying that the space of quantum states (wavefunctions) is L^2(R^3), the space of (square-integrable) complex functions over R^3.

However, then we have to start imposing constraints. e.g., for the free particle in QM we could construct the space of states L^2(R^3), but now suppose that we really only want to quantize a particle that's constrained to move on the surface of a sphere in R^3, or something. Then we have to start chopping down the kinematical Hilbert space to get the physical Hilbert space, the wavefunctions of particles that are constrained to move on the surface of a sphere.

In loop quantum gravity, we start with the kinematical Hilbert space, which has the spin networks as a basis. It is the quantum space of states of connections (modulo gauge transformations). However, not ANY connection corresponds to a solution of Einstein's equation! Only connections which obey the Gauss, diffeomorphism, and Hamiltonian constraints are "physical", connections that represent a gravitational field. So just like we discard connections in the classical configuration space A/G that don't obey the constraints of general relativity, we have to discard states in the kinematical Hilbert space L^2(A/G) that don't obey the quantized versions of those constraints.

So, the diffeomorphism-invariant Hilbert space is what you get when you apply the diffeomorphism constraint to the kinematical Hilbert space. If you also apply the Hamiltonian constraint, you get the physical Hilbert space.

(Note: we applied the Gauss constraint before quantizing by modding out by gauge transformations to consider the space A/G, because it's easy to do that. Then we applied the other constraints after quantizing.)

See also:

http://www.lns.cornell.edu/spr/1999-05/msg0016153.html
http://www.lns.cornell.edu/spr/1999-05/msg0016258.html

Would be good if you could clarify this: It's true that actually the complex SU(2) connection of Ashtekar is not used in LQG, but is used the real SU(3) connection introduced by Barbero?

Well, there are a lot of connections floating around, actually. Some people like Ashtekar's connection. Many use Barbero's nowadays, because you don't have to deal with the reality conditions. Barbero's connection is not SU(3), it is SO(3); you can use an SU(2) connection too, but it's not the same as Ashtekar's connection.

(SU(2) and SO(3) are pretty interchangeable as far as connections are concerned, because they have the same Lie algebra. It can make a difference when global effects are concerned, but loop quantum gravity physicists are usually sloppy about such things.)

 

[marcus]

I was hoping to arrive at some posts expressing intuitive content of loop gravity. Some of us have been reading Livine's thesis and/or work co-authored with Alexandrov or with Freidel.
I find the work admirable but difficult to assimilate. It seems to me that i am gradually having to confront a more completely lorentzian fourdimensional theory----they are extending the group to the whole lorentz group and raising the dimension. How to picture this. Maybe someone else---selfAdjoint, ambitwistor, ... has ideas about how to describe this. Or is it just plain a lot more difficult and tough to describe?

I am used to having 3D connections corresponding to a 3D spatial manifold. Quantum states of 3D geometry. Operators, which presumably can evolve a bit like the Heisenberg picture but without an absolute preferred time, only one operator you choose arbitrarily to serve as clock for the other processes. This is not too bad.

but now Livine etc make us consider 4D connections corresponding to all possible geometries on some 4D manifold. The wave functions are not just functions defined on the connections but on a pair consisting of a 4D connection and a vectorfield χ

any concerns or comments about this new material

 

[Ambitwistor]

Originally posted by marcus
It seems to me that i am gradually having to confront a more completely lorentzian fourdimensional theory----they are extending the group to the whole lorentz group and raising the dimension.

Well, there are many approaches floating around. The 4D approaches are more related to spin foams the usual loop quantum gravity in the canonical approach. It's probably best to start by thoroughly understanding one model, such as canonical LQG with the Ashtekar-Barbero connection, or the Barrett-Crane spin foam model, rather than trying to simultaneously learn about all the different cutting-edge approaches.

 

[marcus]

whether or not it is wise, I would like to understand the role played by this vectorfield chi, let's see how to write it


c

χ

the quantum state or wave function is defined on a pair
consisting of a connection and a vectorfield

Ψ(A, c)

as you say, Ambitwistor, the connection to spinfoam is close, but also there is a connection to the SU(2) loop gravity of the people you mentioned.

I would like to understand how this vectorfield seems to serve as a bridge between the SU(2) and the covariant (i.e. SL(2,C) or lorentzian) approaces

 

[eigenguy]

Originally posted by Ambitwistor
Well, there are many approaches floating around. The 4D approaches are more related to spin foams the usual loop quantum gravity in the canonical approach. It's probably best to start by thoroughly understanding one model, such as canonical LQG with the Ashtekar-Barbero connection, or the Barrett-Crane spin foam model, rather than trying to simultaneously learn about all the different cutting-edge approaches.

I agree, this is excellent advice ambitwistor.

Marcus, if you want your understanding of LQG to advance beyond the impressionistic level it's on now, you really need to commit to just one or two papers on a specific topic and really go over them with a fine tooth comb, proving every intermediate result you can (if you can).

I was advised, quite wisely as it turns out, to look just at the issue of relating polymer and fock states beginning with the pedagogically effective paper I referred you to. You should listen to ambitwistor and jeff. (I must say I'm having an increasingly hard time understanding how you managed that physics expert award thing. Maybe your true calling is politics? )

 

[marcus]

the role of c[

see page 98 of the thesis
a bridge player is discussing the taking of a particular trick

right after equation (8.30) he says
"With the help of a gauge transformation, one notices that it's always possible to rotate a given c(x) to be the same fixed one eg. (1,0,0,0). So an invariant function is completely determined by its section at c=c₀"

and he defines a restricted wavefunction that now depends only on the connection

instead of f(A,c) we are now looking at
f_{χ = χ0}(A), which I will just call f(A) for the moment

"let us remark that f(A) has a residual SU(2) invariance.
Thus we are in the process of studying functions of a lorentz connection, effectively not invariant under SL(2,C) but simply
under the compact group SU(2)!"

Livine's italics and exclamation point. so this is one of the things this vectorfield chi does.

 

[marcus]

Originally posted by marcus
the role of c[

see page 98 of the thesis...

he calls it the "time normal" and makes it one of the configuration variables along with the connection.

he gives some more idea of how he thinks of it right there on page 98, before the part I quoted, before (8.30)

it's a vectorfield with values in the quotient SL(2,C)/SU(2)
that you can think of as a normal to the hypersurface

and he gives a reference to maybe the best article on this
chi "boost" gadget, "time normal" "internal time direction"
the reference is to
http://arxiv.org/gr-qc/0207084
Projected Spin Networks for Lorentz connection: Linking spin foams and loop gravity.
it is dated 12 April, 2003 tho the number suggests earlier.

this 15 page paper (along with the Alexandrov/Livine one we were reading earlier today gr-qc/0205109) might be the best
auxilliary reading to have handy when looking over the thesis. but the thesis is fairly self-contained as such go

 

[selfAdjoint]

Well in the last paper you cite he says the chi field determines the imbedding of the 3-d space Σ in the 4-d spacetime. Which I can see, a field of little vectors normal to that hypersurface and by their direction determining just which shape it takes in 4-space. Then he goes to the network and only keeps the chis at the vertices. And by this he reduces the group action on them from Poincare SO(1,3) (he calls it Lorentz) to a product of rotation groups SO(3) over the vertices. So far so good, it seems to me. If you really want to see the origin of the chis spelled out I guess you would have to go back to Holst's paper (Red Queen, Red Queen!) or the earlier papers by Livine that he cites.

 

[marcus]

Originally posted by selfAdjoint
...you would have to go back to Holst's paper (Red Queen, Red Queen!)

even to stay in one place, in other words, I have to run faster than a bandersnatch, but hey no problem we are always doing that!

 

[marcus]

Loop gravity in plain language

Getting back to the original purpose of the thread, how to introduce loop gravity and spin foams in plain terms---minimum of technicality.

In the "spin foam models" thread a new poster came in today and expressed some curiosity about what was being talked about and I said I would try to do this. Thing is quantizing geometry---in other words general relativity (a theory of changeable geometry that has tested out well)----is on the agenda and amounts to "putting QM and GR together".

Want to say how spin networks and spin foams work in this context.

 

[marcus]

Originally posted by marcus
...amounts to "putting QM and GR together".

Want to say how spin networks and spin foams work in this context.

Space in GR is dynamic--it can change as matter or energy flows around, it can undulate, effects can ripple outwards carrying the news of events that effected the shape of space in some locale. So in quantizing GR one needs a way of describing geometry and the change in geometry.

It will turn out that networks can be used to get a handle on geometries-----to assign probability-like "amplitudes" to the various possible geometries that space can have

a network is basically fairly simple---something like a net or a large ball and stick molecular model---Ashtekar likes to call networks "polymers". A network can have thousands of individual links and vertices---or balls and sticks---or trillions and jillions, so in that sense it is complicated. But in another sense it is simple because made up of simple elements.

have to go, but will get back to this later

 

[marcus]

...a network is...something like a net or a large...molecular model---Ashtekar likes to call networks "polymers". A network can have thousands of individual links and vertices...so in that sense it is complicated. But in another sense it is simple because made up of simple elements.

there are several different ways to tell the story, here's one. A network by itself is rather amorphous---it lacks geometry. all it is is a bunch of points with a list of which pairs of points are connected (in which direction, to make later work simpler there is a preferred direction, the links are one-way-street type)

it doesn't have fixed angles or lengths written onto its links so it doesn't define shape by itself, but you can get a whole lot of different possible geometries to live on it, by assigning data to the links, like angles but not exactly angles.

What's done is to choose a GROUP of ways to twist and turn as you run along any link from point A to point B. This group is called G and it is usually some group of 2x2 matrices---you can write down all kinds of rotations with a mere 2x2 matrix and even other simple actions like expansions and contractions etc. There are several different groups of 2x2 matrices some larger with more varied action and some smaller and there is some range of choice in doing the theory.

Think of the matrices in the group as rotations and imagine that you go all thru the network and label each link with a group element that describes a "rotation" or something more general that happens when you run along that link.

That assignment of one group element to each link in the web can be called a (discrete) "connection".
Intuitively it connects how things are oriented around one node in the web with how they are oriented at the neighbor node just down the street.

A discrete connection is a stripped-down version of a much fancier bigger machine that lives on a smooth manifold, a continuum. If you were to plunge our finite network into a continuum, where an official bigtime connection was living, then IT would induce a discrete connection on our network which would be a kind of meager skeleton or no-frills diagrammatic sketch of the original. But let's not bother to define exactly what a manifold is or what the usual idea of connection is in differential geometry. Our stripped-down finite skeletal idea is workable.

(Indeed I got the discrete connection idea from E.R.Livine's thesis and some of the articles around it, it may actually turn out to work better for some things!)

Imagine a web with E links and V nodes (the E stands the word "edge" which is sometimes used for the links in a network, and V for vertex). A connection, at least before it comes to live on the graph, is just a list (g1, g2,...gE) of group elements. So if you like cartesian product set-notation the space of all possible connections which could be chosen for this particular web is
GxGx...xG = G^E

I am telling you this set of connections because the theory defines its core hilbertspace on it. That is the basic thing in any quantum theory---that space and the operators on it. But first, since that is a bit technical, can you see how that in some sense this collection of all possible connections (each one telling a specific way things twist and turn as you run thru the network) is tantamount to the range of possible geometries?

 

[marcus]

Things keep happening in quantum gravity and I don't have a sticky here where I can keep the useful source material handy or post recent
developments. So I'll try using this thread.

Rovelli just posted a new draft of his book "Quantum Gravity". It is the November 25 draft and is quite a bit changed from the August draft some of us were reading earlier. the contract for publication has been signed with Cambridge University Press.

We were discussing stuff from Livine's thesis in this and another thread.
http://arxiv.org/gr-qc/0309028
Girelli and Livine have come out with a paper about quantizing speed.
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

Ichiro Oda has posted "A Relation Between Topological Quantum Field Theory and the Kodama State"
http://arxiv.org/hep-th/0311149
The last sentence of the "Discussion" section at the end of the paper reads: "Of course, one of the big problems in future is to clarify whether the Lorentzian Kodama state is normalizable under an appropriate inner product or not." It is clear that he is specifically interested in applications to general relativity---he mentions loop quantum gravity in the first paragraph and refers to gravity/GR at several points in the paper. This paper can be seen as Oda's careful response to an earlier paper by Witten gr-qc/0306083.
Witten said Kodama was not normalizable (in whatever inner product Witten thought was appropriate) and Oda does not buy this and says politely that the question is still open---is, in fact, the "big problem in future".

Daniele Oriti's thesis is out
http://arxiv.org/gr-qc/0311066
"Spin Foam Models of Quantum Spacetime"

Smolin and Starodubtsev have posted a brief paper which writes the actions for Palatini GR and Ashtekar GR and BF topological QFT and also another (FΛF) type of TQFT all in the same formula. There is a dynamic variable which as it changes seems to make the system change smoothly from one theory to another

"General Relativity with a topological phase: an action principle"
http://arxiv.org/hep-th/0311163

I found some family resemblance between this paper and Oda's--but both are quite recent and neither cites the other.

The cosmological constant occurs in a number of recent quantum gravity papers. The one by Girelli/Livine is one of the most recent. One of the most basic--perhaps a landmark---is Karim Noui and Philippe Roche "Cosmological Deformation of Lorentzian Spin Foam Models"
http://arxiv.org/gr-qc/0211109

 

[marcus]

ongoing BH vibration mode saga

A paper by a couple of New Zealanders
http://www.arxiv.org/abs/gr-qc/0311086
points out a discrepancy between two ways that people have used
to calculate BH quasi-normal modes ("ringing frequencies")
and attempts to resolve the discrepancy by "critically re-assessing"
the approach used by Motl and Neitzke
the issues are still shifting around the area operator in loop gravity
and the Immirzi parameter which occurs in some versions
but not all (e.g. the covariant version used by some people such as Livine/Alexandrov/Noui/others?) what happens to the spectrum of the area operator in covariant loop gravity and how does that compare with the results (themselves not yet conclusive) for BH vibration modes?

 

[lumidek]

New Zealanders

Dear Marcus,

I always appreciate your interest and your qualified comments about physics - and not only the technical ones. Let me just say a couple of words about your new explanation. The current paper

http://www.arxiv.org/abs/gr-qc/0311086

is pretty far from the original proposals by Shahar Hod and Olaf Dreyer because no results - except for the four-dimensional Schwarzschild black holes in the infinite space - provide us with evidence of Hod's and Dreyer's conjectures. Everything else seems to contradict the general predictions by Hod and Dreyer (about the asymptotic real part of the quasinormal modes).

When you wrote that the authors "critically re-assess the approach used by Motl and Neitzke", you are twisting the words to get a very different meaning. The New Zealanders do not claim that there is anything wrong with our monodromy calculation done with Andy Neitzke! They are saying that something is probably wrong with a paper by Castello-Branco and Abdalla who did not use our methods carefully.

To claim - today - that our results with Andy are wrong would not be the most reasonable thing to do because essentially all of our results have been confirmed numerically - for example, our prediction for the Reissner-Nordstrom black holes was confirmed beautifully by colleagues like Berti, Kokkotas, Cardoso, Lemos and others (after our paper).

I and Andy used the so-called monodromy method, and as far as I know everyone agrees that it works correctly in the contexts that we studied in our paper. Of course, not only our results, but also the method can be useful for other people and other problems. However we can't guarantee that the results obtained by other people, using our machinery, will be correct.

I found some of the results in the Schwarzschild-de-Sitter context a bit counter-intuitive, and there have been many papers about the Schwarzschild-de-Sitter black hole. (Our paper with Andy was never about de Sitter, all the black holes that we studied were in empty space.)

The New Zealanders mostly criticize the paper by Castello-Branco and Abdalla [19]

http://arxiv.org/abs/gr-qc/0309090

Yes, I also think that they used our method a little bit blindly. Their results looked too similar to the case of the flat space. The New Zealanders claim that the method can't be used - at least not in this way - if two horizons coincide, and I tend to agree with that. Moreover, there are many questions about the choice of the boundary conditions.

The quasinormal modes remain a lively topic. You can observe a rather complete list of the developments if you look which papers cite e.g. my first paper:

http://www.slac.stanford.edu/spires/find/hep/www?c=00203,6,1135

Once again, be sure that none argues that my results or our results with Andy (and the methods used to derive them in our context) are incorrect. The newer papers study more complicated cases where some errors have been done - but not by me and Andy.

Best wishes
Luboš

 

[selfAdjoint]

Welcome to the Physics Forums, Lubos. We're honored to have you here.

 

[marcus]

Originally posted by selfAdjoint
Welcome to the Physics Forums, Lubos. We're honored to have you here.

Indeed so! and thanks for making the distinction between your work and the use of a similar method by others which, you say, the New Zealanders were examining critically. Any more explication you can give would, I suspect, be much appreciated.

best wishes,
marcus

 

[marcus]

useful (GR-based) quantum gravity links, continued

Things keep happening in quantum gravity and there is no sticky here to keep handy links to source material about loop gravity developments. So I continue trying to use this thread.

The term "Loop Gravity" is used for want of a better one for a broad range of research approaches to quantizing general relativity.

Rovelli briefly discusses "the name of the theory" on page (xvi) of his new book. The name "loop" is something of an accident because current approaches are not so much concerned with loops. But no one has come up with a good alternative.

The main things the new approaches seem to have in common is that they emerge from General Relativity (rather than Particle Physics) and that they aren't string/brane theories.

A kind of merging among topological QFT ("TQFT") and non-commutative geometry (especially because of the Cosmological Constant) and spinfoams and (Lorentzian spin network-based) LQG seems to be in process. Some people seem to have found a way to do spin network analysis with non-compact groups---so they can use SL(2,C) for gauge in place of SU(2)---hep-th/0205268. Some of this may matter or may not, seems too early to judge. But it might help to keep some of the links handy for reference.

Today Lubos Motl posted a message to Non-unitary ("somewhere in the tropics") containing one link. This link was offered as a characterization of LQG. It was to a 5-year old 11-page paper by Rovelli and Upadhya which was intended as a quick into. They call it a "Primer" to the subject. It does not really characterize the field of loop gravity but Lubos might appreciate it if I include the link in this "sticky" list of links so here it is:

Rovelli/Upahya 5-year-old brief 11-page "primer" to the subject
http://arxiv.org/abs/gr-qc/9806079

Rovelli just posted a new draft of his book "Quantum Gravity". It is the November 25 draft and is quite a bit changed from the August draft some of us were reading earlier. the contract for publication has been signed with Cambridge University Press. The PDF file for Rovelli's book is at his homepage
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
It takes about 10 minutes to download and convert so that it can appear on the screen. It is 300 plus pages long.

The SPIRES database on citations is often handy. There is a topcited list for the smaller series GR-QG (general relativity and quantum gravity) as well as for the huge series HEP-TH.
http://www.slac.stanford.edu/library/topcites/topcites.review.2002.html

We were discussing stuff from Livine's thesis in this and another thread. Here is Livine's thesis. He does a lot with explicitly covariant---SL(2,C)-style---spin networks and makes an explicit bridge from LQG to Lorentzian spinfoams.

http://arxiv.org/gr-qc/0309028

Girelli and Livine have come out with a paper about quantizing speed.
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

Ichiro Oda has posted "A Relation Between Topological Quantum Field Theory and the Kodama State"
http://arxiv.org/hep-th/0311149
The last sentence of the "Discussion" section at the end of the paper reads: "Of course, one of the big problems in future is to clarify whether the Lorentzian Kodama state is normalizable under an appropriate inner product or not." This paper can be seen as Oda's careful response to an earlier paper by Witten gr-qc/0306083.
Witten said Kodama was not normalizable (in whatever inner product Witten thought was appropriate). Apparently Oda does not buy this and says politely that the question is still open---is, in fact, the "big problem in future".

Daniele Oriti's thesis is out
http://arxiv.org/gr-qc/0311066
"Spin Foam Models of Quantum Spacetime"

Smolin and Starodubtsev have posted a brief paper which writes the actions for Palatini GR and Ashtekar GR and BF topological QFT and also another (FΛF) type of TQFT all in the same formula. There is a dynamic variable which as it changes seems to make the system change smoothly from one theory to another

"General Relativity with a topological phase: an action principle"
http://arxiv.org/hep-th/0311163

I found some family resemblance between this paper and Oda's--but both are quite recent and neither cites the other.

The cosmological constant occurs in a number of recent quantum gravity papers. The one by Girelli/Livine is one of the most recent. One of the most basic--perhaps a landmark---is Karim Noui and Philippe Roche "Cosmological Deformation of Lorentzian Spin Foam Models"
http://arxiv.org/gr-qc/0211109

 

[marcus]

this is the substitute for a sticky to keep links to current
Quantum Gravity resources, so I will update it from time to time.

QG Phenomenology seems to be attracting research interest (as prospects emerge for testing Planck-scale effects)
the best and most recent survey of it that I have found is a November article by Giovanni Amelino-Camelia called

"Quantum Gravity Phenomenology"

http://arxiv.org/physics/0311037

It is 8 pages and was prepared in tandem with an article he wrote for the November 2003 issue of "Physics World". This issue was devoted to the current state of affairs in Quantum Gravity and had 3 invited survey articles, one on phenomenology (prospects for testing the theories) by Giovanni A-C, one on LQG by Carlo Rovelli, and one on string by Leonard Susskind.

 

[marcus]

There is a major issue within LQG about how energy and momentum transform under the Lorentz group. The two different points of view are exemplified by

Rovelli and Speciale "Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction"
http://arxiv.org/gr-qc/0205108
this was published in 2003 in Physics Review D.

Magueijo and Smolin "Generalized Lorentz invariance with an invariant energy scale"
http://arxiv.org/gr-qc/0207085
this was also published in 2003 in Physics Review D.

The two versions yield different predictions about dispersion in arrival time of gammaray bursts. It is barely possible that GLAST may be able to distinguish between the two approaches to building loop quantum gravity theory when it starts up in 2006.

The nub of the issue is that the Planck length (or area, or energy) plays a crucial role as marking where quantum gravity effects become dominant. But relatively moving observers see lengths and areas differently! How can one reconcile having a theory locally embodying the principle of relativity (no preferred frame, all observers equal) that nevertheless has a certain length (or energy) as an important landmark?

Intuitively, just as in 1905 SR where the speed of light is the same for all observers, this other landmark the Planck energy should be the same for all observers! But how can one manage this? So there is this internal debate in LQG on how to accommodate this and maybe observational data will help settle it

[edit: I checked on the launch date for Gammaray Large Area Space Telescope, GLAST, and it is not until 2006]

 

[marcus]

another for the surrogate sticky

According to Loren B's post on another thread, the January 2004
issue of Scientific American has an article that (at least in part)
deals with Loop Gravity. I haven't seen it. Don't know if there is a web reference.

It seems like it might be a useful article to add to the list here, as a recent survey for wide audience. Does anyone have more information? The article is by Lee Smolin


[edit: I found a link to a two-paragraph teaser for the article
http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=00012BDE-E7EA-1FD3-A7EA83414B7F012C
more than that, and the crafty editors of digital SciAm want us to pay for it]

 

[nonunitary]

The Sciam issue seems to be interesting. Too bad one cannot get it online!

By the way, there is a link in the General Relativity Hyperspace
where forthcoming events are announced:

http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference

There is also a workshop on Loop Quantum Gravity announced there, apart from the preliminary programme for GR17.

 

[marcus]

17th International Conference on General Relativity

Originally posted by nonunitary

By the way, there is a link in the General Relativity Hyperspace
where forthcoming events are announced:

http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference

There is also a workshop on Loop Quantum Gravity announced there, apart from the preliminary programme for GR17.

Thanks! I followed the link you gave to:
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?conference
and saw the announcement of "Loops and Spinfoam" conference in May 2004 in Marseille, organized by Rovelli, Freidel, and Roche.
and also the program you mentioned, for the 17th International Conference on General Relativity at:
http://www.maths.qmul.ac.uk/wbin/GRnews/conference?03Dec.8
to be held in Dublin on 18-24 July 2004.

 

[nonunitary]

Hi,
One can also see the most recent announcements at:

http://www.maths.qmul.ac.uk/wbin/GRnewslist/conference?10

where another LQG event is advertised.
I followed the links at the site of the organizers and found the
page:

http://www.nuclecu.unam.mx/~corichi/lqg.htm

Bye

 

[marcus]

Originally posted by nonunitary
...
http://www.nuclecu.unam.mx/~corichi/lqg.htm
...

Thanks again! this Mexico City symposium on loop and spinfoam
is really interesting news. I like the list of people
who have already said they would attend. One could learn more about quantum gravity, maybe, in Mexico Jan30-Feb1 next year than one might in Dublin in July with the 17th International Conference. I will copy the program planned for this long-weekend loop/foam symposium, from your link:

1. Spin foam models
(to include 2+1 and 3+1 theories; limitations of the Barrett-Crane
model; relation to the canonical approach to dynamics; the role of
the Barbero-Immirzi parameter; canonical and spin foam geometries; issue
of the `continuum limit', renormalization group flows)

2. Status of the Hamiltonian constraint
(to include 2+1 and 3+1 theories; spin-foam and Thiemann-type
approaches; quantum cosmology; Semi-classical corrections to
Einstein equations; factor ordering; too many solutions?
issue of finding solutions and inner product, the "phoenix project").

3. Semi-classical issues
(to include relation between kinematical and dynamical semi-classical
states; quantum field theory on quantum geometry; quantum cosmology;
Minkowski coherent state and Minkowski spin foam)

4. Loop quantum phenomenology
(to include Lorentz invariance;`Double special relativity'; quantum
cosmology; Kodama state and de Sitter background)

5. Conceptual issues
(observables through matter coupling, string theory in polymer
representation; matter couplings on semi-classical states of
geometry and string theory; issue of time; meaning of histories used
in spin foam, role of quantum groups is LQG)

 

[marcus]

Originally posted by marcus

4. Loop quantum phenomenology
(to include Lorentz invariance;`Double special relativity'; quantum
cosmology; Kodama state and de Sitter background)

the programme for the Mexico City symposium is a good "weather-vane" to point out what the interesting questions are now.
Loop quantum phenomenology seems to have some important issues.
Especially around DSR and GLAST and possible variations in photon time of flight over cosmological distances.
the person who has the most to say about this for me now is
in Wroclaw Poland, name of Jurek (Jerzy) Kowalski-Glikman

"Velocity of particles in Doubly Special Relativity"
http://arxiv.org./abs/hep-th/0304027

"Doubly Special Relativity and quantum gravity phenomenology"
http://arxiv.org./abs/hep-th/0312140

http://www.ift.uni.wroc.pl/JK-G/

Jerzy K-G has published (in 2001) with Amelino-Camelia and he has published (in 2003) with Freidel and Smolin. I think he understands DSR more as a mathematician, more rigorously and clearly than Amelino-Camelia who initiated the research into it and originally conceived of it! I am impressed by these two papers. It looks to me as if he basically just takes control of DSR and contradicts Smolin and Amelino-Camelia. the way Jerzy K-G develops DSR it does what it is supposed to--there are two observer-independent scales one of speed and one of energy--and also the speed of a gammaray photon does NOT change with energy: it stays c for all photons, indeed all massless particles. This "Polish" version of DSR will be destroyed if it turns out in 2006 that GLAST does after all see any speed-variation in high-energy photons, so the Polish version of the theory is firmly and directly falsifiable. Have to say I like it. Alejandro Corichi should make sure K-G comes to the Mexico City symposium for topic 4 "Loop quantum phenomenology"

 

[selfAdjoint]

Say, Marcus, it really looks like we PFers are pretty up to speed on the stuff they are going to have on that program. Thanks mostly to you, I might add. Great going!

 

[marcus]

Originally posted by selfAdjoint
Say, Marcus, it really looks like we PFers are pretty up to speed on the stuff they are going to have on that program. Thanks mostly to you, I might add. Great going!

by "you" you have got to mean Meteor, Nonunitary, yourself, Ambitwistor as well, to mention only the first that come to mind. Thanks to all. I didnt realize until today what a key role Jerzy K-G is playing. Look at the program from the Wroczlaw Institute of Theoretical Physics for the "40th Winter School in Theoretical Physics" for Feb 4-14, 2004. Each year since 1964 they have had a winterschool gathering a dozen or so worldclass people at this
ski-resort. this year the topic chosen is "Quantum Gravity Phenom."
Steve Carlip is one of the organizers, and so is (you guessed it) Jerzy Kowalski-Glikman.

Speakers:

E. Alvarez Quantum Gravity
G. Amelino-Camelia Introduction to quantum gravity phenomenology
P. De Bernardis Cosmology with BOOMERANG, WMAP
A. Grillo Planck-scale kinematics and the Pierre Auger Observatory
T. Jacobson Astrophysical bounds on Planck-supressed Lorentz violation
J. Kowalski-Glikman Introduction to doubly special relativity
C. Laemmerzahl Tests of Lorentz symmetry in space and interferometry
P. Lipari Ultra-high-energy cosmic-rays
J. Martin Trans-Planckian cosmology
N. Mavromatos PCT symmetry and quantum gravity phenomenology
T. Piran Gamma-ray bursts
J. Pullin Canonical quantum gravity phenomenology
L. Smolin Cosmological constant in Quantum Gravity

The names Ted Jacobson and Nick Mavromatos especially ring a bell as they've been writing papers about QG phenomenology, various kinds of astronomical tests, that other people cite regularly. IIRC Mavromatos co-authors with Ellis. But I guess so does Pullin and Lipari and several others, ring a bell I mean

So much is going on! end-January Mexico City (loop/foam symposium)
first half of February Karpasz School (QG phenomenology)
then Freidel and Rovelli's Loop Gravity/Spinfoam conference at Marseille May 3-May 7
then the July thing at Dublin--17th International General Relativity conference

Good thing nonunitary provided the links to these things. Yours truly had not registered all the activity.

 

[meteor]

Well, given that my knowledge in differential geometry is rather poor, I've ordered the book "Differential geometry" of Schaum to Amazon. Hope that will be a good book, like all the other Schaum books that I've read
A question: Then the SO(2) connection used like a variable in Ashtekar's general relativity is a real connection or a complex connection? There are papers that say that is real and others that is complex. I'm dying in the doubt
I've just read that loop quantum gravity violates the "weak energy condition" at short distances, when the granularity of spacetime becomes significant. I've don't have the foggiest idea of what is the weak energy condition, so I'm going to read about it right now

 

[marcus]

Hi Meteor, I started a thread with your two questions
1. about Ashtekar's new variables
2. about "weak energy condition"
Both could lead to discussion and I am trying to save this thread as a kind of "sticky" for useful links, source material, conference news, and so on. Hope it is OK for me to make a separate thread for what you asked about. You will see it.
I called it "Loop gravity---two questions"