Loop-and-allied QG bibliography

[lumidek]

Sorry

Dear Marcus,

I see, sorry. I made a too quick conclusion that you share the only approach that I consider reasonable in this question.

It's great to keep an open mind, but if Hawking is correct, a lot of ideas can evaporate from a mind that is too open.

All the best
Luboš

 

[marcus]

Originally posted by meteor
... I will post this one:
"Comparison of area spectra in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0401110
Abstract:
We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these spectra. For one of these spectra - the equally-spaced spectrum - we show in light of a proposed connection of the black hole area spectrum to the quasinormal mode spectrum that this spectrum is completely consistent with this connection. This follows without requiring a change in the gauge group of the spin degrees of freedom in this formalism from SU(2) to SO(3).

This is the paper by Gilad Gour and V. Suneeta (both at U Alberta
Edmunton) that Meteor called to our attention.

An objection raised earlier seems not to apply since, while the area spectrum is discrete (as usual in LQG) and evenly spaced, the spacing is microscopic (planck-scale) and not fundamentally very different from the un-evenly spaced. This paper could be important and needs a more careful look. So let's look at Gour/Suneeta equations (2) and (3)

These are the two competing formulas for the area of a surface S.

the first is in the non-evenly spaced (NS) case

A_S = 8\pi l_P^2 \gamma \Sigma \sqrt{j_n(j_n + 1)}

the second is in the evenly spaced (ES) case

A_S = 8\pi l_P^2 \gamma \Sigma (j_n + 1/2)

We are talking about a spin network state and a physical surface, S, defined by some material object. The spin network state has N edges which intersect the surface and each edge contributes a bit of area to the sum. The intersecting edges are indexed n = 1,...,N.

Oh yeah, l_P² is the Planck unit of area, the square of the Planck length

Equation (2) is the standard 1994 result of Rovelli and Smolin. A priori one wonders how Gour/Suneeta could possibly be challenging this by proposing a different formula for the area, namely equation (3).

Furthermore their proposal may make some people nervous since it results in a value of ln 3/3pi for the Immirzi parameter. As it happens this doesn't bother me. Some versions of LQG don't even have an Immirzi parameter: Loop theories are under construction and there is still room for variation in the parameters and even some surprises. So I am not going to dismiss this out of hand just because of some number being an unfamiliar ln 3/3 pi instead of the more usual value that has been around longer.

Anyway Meteor posted the link to this a few days ago so let's see what it is about.

 

[marcus]

common sense suggests there may be pitfalls in Gour/Suneeta approach.
the other formula goes back to 1994. why would Rovelli/Smolin have chosen their more complicated formula unless there were some reason?
but so far so good.
anybody (Meteor?) who wants to help read thru this short (7 page)
paper is invited

a couple of more links on the area issue:

Alexios Polychronakos
Area spectrum and quasinormal modes of black holes
http://arxiv.org/hep-th/0304135

Alekseev, Polychronakos, Smedbaeck
On the area and entropy of a black hole
http://arxiv.org/hep-th/0004036

Alexkseev and Smedbaeck are at the Institute for Theoretical Physics, Upsala University, in Sweden
Polychronakos is at the University of Ioannina in Greece and also the
CUNY Physics Department in the USA.

These seem to be the dangerous people we were warned about earlier. They think that, just as an atom while it is in a heat bath in equilibrium at a given temperature can radiate with a black body spectrum but by itself radiates a line spectrum, so a black hole not surrounded by radiation and therefore not in equilibrium with its surroundings may in fact radiate a line spectrum. Over much of the spectrum it would strongly resemble black body but at low frequencies it would deviate and become more obviously liney.

Polychronakos says, in "Area spectrum and...", for instance)

-------quote from page 9----------

We do not feel that this is damning. The high-frequency exponential part of the spectrum is accurately reproduced, the discreteness there being inconsequential. This is the energy range in which the photons (or other emitted particles) behave essentially like classical particles, whose scattering properties are expected to be accurately reproduced by the classical black hole metric. For frequencies close to the thermal frequency, however, the wavelength of the photons becomes comparable to the size of the black hole and they sense global properties of its geometry. Backreaction due to geometry change at emission and absorption of such photons is expected to be important, the energy of these photons being of the same order as
the energy spacing of the black hole. A deviation from ideal black-body spectrum, which assumes a fixed metric and ignores back-reaction, would seem reasonable.

-----end quote----------

 

[meteor]

If my opinion counts, (I'm only an amateur, not a high-level physicist) I don't like the idea of the equally-spaced area spectrum, because it means that practically all the contributions to the black hole area comes from edges carrying a representation of 1. Would be desirable to know why the representations=1/2 are excluded from puncture the black hole area

 

[marcus]

Originally posted by meteor
If my opinion counts..

you found the paper and put it in for discussion
so your opinion doesn't count?

Gour/Suneeta cite Polychronakos (hep-th/0304135)
which I am finding the easiest to read and the
most helpful. (the subject is new to me, maybe to
you as well)

On page 8 Polychronakos says
"To summarize...if the standard counting formula for states (6) is
assumed, then the equidistant area spectrum as proposed in [14]
naturally explains the domination of spin-1 links
and reproduces the ringing mode properties of black holes, without
the need to eliminate half-integer spins..."

You say "...would be desirable to know why spin-1/2" are excluded. It is a good question but, according to him, they are not eliminated arbitrarily or "by hand".
He says there is no need to exclude them, because statistically the spin-1 punctures are more prevalent.
Why? this is what I am wondering. He says there is a natural explanation for why spin-1 is more prevalent and predominates over the other. The explanation is on page 5, I think. Around equations (12) and (13). It is very brief and does not seem hard.
It seems to depend on the semiclassical result of Hod!
Hod made an important contribution to Loop gravity with his number
4ln3, which Motl, fortunately enough, was able to confirm by a direct calculation. It has added interest to the field and given them something to work on, and here it is showing up again on page 5 of Polychronakos.

 

[meteor]

Another paper:
"Beyond space and time"
http://arxiv.org/abs/physics/0401128
Author: Ruediger Vaas
Abstract:
"The secret network of the universe: How quantum geometry might complete Einstein's dream. - An informal introduction to quantum geometry (loop quantum gravity), spin networks, quantum black holes, and the work of Abhay Ashtekar, Carlo Rovelli, Lee Smolin and others."

After a quick inspection, I'm amazed: You will not find a single equation in the text!

An interesting phrase of the text: "If one could observe nature with maximum possible enlargement, space and time would dissolve and the granular mesh of the spin network would come to light ( or more precisely: the quantum physical superposition of all possible configurations of these entities)"

 

[marcus]

Originally posted by meteor
Another paper:
"Beyond space and time"
http://arxiv.org/abs/physics/0401128
Author: Ruediger Vaas

My suspicion about that article is that
Rudy Vaas is a science-journalist, and it was
written for the German public to run in
the popular press. In English it sounds "over-the-top"
in places, but a good editor could fix that.

Amitabha Sen translated it into English.
Sen is a reputable theoretical physicist.
In 1982 he started the line of development that
resulted in Ashtekar's 1986 "new variables"
approach. Maybe the new variables should
be called "Ashtekar-Sen"

It could be a good popularization article if
it were edited to tone down the journalistic excess.

 

[marcus]

Originally posted by meteor

"Comparison of area spectra in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0401110

Abstract:
We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole...

I've come to the conclusion that we should have a thread about the "equidistant spectrum" version LQG area.

this is about the reasoned opposition of ideas
the majority Loop people say the Rovelli/Smolin spectrum
which is not equidistant or "evenly spaced".
But a few people say to look at the evenly spaced spectrum
and they seem to have a case to make

the papers by Polychronakos
and by him and Alekseev etc
seem pretty clear and interesting too
as well as the one Meteor brought.

here are those other two links:

Alexios Polychronakos
Area spectrum and quasinormal modes of black holes
http://arxiv.org/hep-th/0304135

Alekseev, Polychronakos, Smedbaeck
On the area and entropy of a black hole
http://arxiv.org/hep-th/0004036

 

[meteor]

http://xxx.soton.ac.uk/abs/gr-qc/0401122
The Pauli Exclusion Principle and SU(2) Versus SO(3) in Loop Quantum Gravity
Author: John Swain
Abstract:
"Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not."


In this paper, Swain tries to incorporate some kind of Pauli exclusion principle to LQG: If only at most two edges of j=1/2 are allowed to puncture a given surface, then the predominance of edges j=1 puncturing the horizon of a BH is naturally explained

 

[marcus]

Updating the Surrogate Sticky

Meteor thanks for the John Swain article. It seems as if there are a number of interesting possible reasons that the spin 1 edges play such a prominent role in the black hole horizon area.

We are now at page 10 of this thread and many of the links were gathered back on page 7, so I will update things and bring the earlier links forward:
--------------------------------

So far there is no sticky for Loop Gravity reference links. And this thread is serving as a surrogate "reference library". Thanks to all who have contributed so far!

The term "Loop Gravity" is used for a broad range of background-independent 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 historical accident---current approaches are not so much involved with loops as with spin network states. But no one has come up with a collective designation that includes spin foams and is more convenient.

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.

-------Loop Gravity texts--------
Rovelli posted the 30 December 2003 draft of his book "Quantum Gravity", to be published this year by Cambridge University Press.
The PDF file is at his homepage
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html.
The book is around 350 pages long and takes a few (like ten?) minutes to download and convert.
To download the 30 December 2003 draft of the book directly:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Here are Thiemann's Lecture Notes (they have been published in Berlin by Springer Verlag)
"Lectures on Loop Quantum Gravity".
A draft is online at
http://arxiv.org/gr-qc/0210094

---------some current work------
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

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

Smolin and Magueijo
"Gravity's Rainbow"
http://www.arxiv.org/abs/gr-qc/0305055
(this was revised and reposted 3 February 2004,
I haven't read the revised version yet)

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

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

-------Quantum Gravity Phenomenology---------

three recent papers:

Giovanni Amelino-Camelia
"A perspective on quantum gravity phenomenology"
http://www.arxiv.org/abs/gr-qc/0402009
dated 2 February 2004

Giovanni Amelino-Camelia, Jerzy Kowalski-Glikman, Gianlucca Mandanici, and Andrea Procaccini
"Phenomenology of Doubly Special Relativity"
http://arxiv.org/gr-qc/0312124
dated 30 December 2003

Jerzy Kowalski-Glikman
"Doubly Special Relativity and quantum gravity phenomenology"
http://arxiv.org/hep-th/0312140
dated 12 December 2003

Jerzy Lukierski
"Relation between quantum κ-Poincare framework and doubly special relativity"
http://arxiv.org./hep-th/0402117
dated 18 February 2004

other fairly recent ones:

Jerzy Kowalski-Glikman and Sebastian Nowak
"Doubly Special Relativity and de Sitter space"
http://arxiv.org/hep-th/0304101
dated 11 October 2003

M. Daszkiewicz, K. Imilkowska, J. Kowalski-Glikman
"Velocity of particles in Doubly Special Relativity"
http://arxiv.org/hep-th/0304027
dated 3 April 2003


---------Loop Quantum Cosmology-------

as a background reference for classical (non-quantum) cosmology:
Charles Lineweaver
"Inflation and the Cosmic Microwave Background"
http://arxiv.org/astro-ph/0305179
dated 12 May 2003

Martin Bojowald
"Loop Quantum Cosmology: Recent Progress"
http://arxiv.org/gr-qc/0402053
One of the invited plenary talks at the January 2004 ICGC
conference (see list of recent conferences)


Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology and Boundary Proposals"
http://arxiv.org/gr-qc/0312103
dated 23 December 2003

Martin Bojowald
"Quantum Gravity and the Big Bang"
http://arxiv.org./astro-ph/0309478
dated 17 September 2003, briefly summarizes how
LQG can serve to cure the big bang singularity and
motivate inflationary expansion. Short and less technical
than the other two papers.

Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology, Boundary Proposals, and Inflation"
http://arxiv.org/gr-qc/0303072
dated 19 March 2003

Shinji Tsujikawa, Parampreet Singh, Roy Maartens
"Loop quantum gravity effects on inflation and the CMB"
http://arxiv.org/astro-ph/0311015
from the Tsujikawa/Singh/Maartens abstract:
"In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early kinetic-dominated super-inflation phase, with a quantum-corrected Friedmann equation. As a result, an inflaton field is driven up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyze the cosmological perturbations and show that loop quantum effects can leave a signature on the largest scales in the CMB, with some loss of power and running of the spectral index."


-------recent conferences------

Strings meet Loops (Albert Einstein Institute, MPI-Potsdam) October 2003
http://www.aei-potsdam.mpg.de/events/stringloop.html

Loop Gravity Workshop (Mexico City) January 2004
http://www.nuclecu.unam.mx/~corichi/lqg.htm

International Conference on Gravity and Cosmology (India) January 2004
http://www.cusat.ac.in/icgc04/

Quantum Gravity Phenomenology, (40th annual Polish Winterschool in Theoretical Physics) February 2004
http://www.ws2004.ift.uni.wroc.pl/html.html

--------upcoming conferences--------

Loop/SpinFoam Conference (Marseille) May 2004
http://www.maths.qmul.ac.uk/wbin/GRnews/conference?03Aug.1
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?10

General Relativity Conference (Dublin) July 2004
more annoucements at
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?conference

----------fundamental constants, Planck units, time-keeping-------
In December 2003, the National Institute of Standards and Technology (NIST) posted new CODATA recommended values for the basic Planck units

http://physics.nist.gov/cuu/Constants/

choose "universal" from the menu to find (among other things) the recommended values of
planck mass
planck length
planck time
planck temperature

A 1997 article on timekeeping, discussing GR effects allowed-for in the GPS
http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf


------projected observational means for testing quantum gravity------

Floyd Stecker
"Cosmic Physics: the High Energy Frontier
http://arxiv.org/astro-ph/0309027
dated September 2003

Stecker discusses the various earth-based and orbital instruments, currently operating, or under construction, or planned, or proposed, and the kind of data becoming available. Among many other things he discusses GLAST, planned to start operating 2007, which, if there are tiny energy-dependent differences in speed among gamma-ray-burst photons, may be able to detect same. Also discusses neutrino observation.
========
simply to have this link handy:
https://www.physicsforums.com/misc/howtolatex.pdf

 

[marcus]

current research numbers ("demographics")

In another thread the question of "majority consensus" (or one might say "research demographics") came up again.
Numbers of papers, or even numbers of blockbuster papers that get lots of follow-up citations, don't necessarily mean all that much but the issue gets raised now and then so we should have some kind of objective data. There is a small and increasing output of papers in Loop Gravity:

Curious about quantifying this, I went to arxiv.org "Search Physics Archives" page and put in [ABS = loop quantum gravity]OR[ABS = spin foam]OR[ABS = loop quantum cosmology] since 2000. The engine found
these numbers of papers:

2000 46
2001 48
2002 64
2003 70

Y(2/11) 73*

These are the preprints at the archive that have somewhere in their ABSTRACTS either the words loop quantum gravity, or the words spin foam, or the words loop quantum cosmology.
--------------

Although I'm not especially interested in string/brane theories, some people seem interested in comparisons so here's the same numbers for
[ABS = string]OR[ABS = brane]OR[ABS = M-theory]


2000 1457
2001 1496
2002 1500
2003 1265

Y(2/11) 911*

That is, those where the abstract summary of the paper has in it somewhere the word string, or the word brane, or the word M-theory.

*The search engine also has a "Past Year" option which gives the papers posted in the year-to-date: the preceding 12 months. On February 11 I ran the same check for year-to-date and got corresponding numbers for the "Year to 2/11" which I've listed here separately as Y(2/11).

Y(2/11) reflects activity in part of the calendar year 2003 and in part of the calendar year 2004.

 

[marcus]

recent work on the area spectrum

Meteor started us collecting recent work bearing on
the vibration of black holes and the Loop Gravty area spectrum.


Gilad Gour and V. Suneeta
"Comparison of area spectra in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0401110

Alexios Polychronakos
Area spectrum and quasinormal modes of black holes
http://arxiv.org/hep-th/0304135

Alekseev, Polychronakos, Smedbaeck
On the area and entropy of a black hole
http://arxiv.org/hep-th/0004036

Gour and Suneeta are at the University of Alberta.
Alexkseev and Smedbaeck are at the Institute for Theoretical Physics, Upsala University, in Sweden
Polychronakos is at the University of Ioannina in Greece and also the
CUNY Physics Department in the USA.

Setare and Vagenas
"Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes"
http://arxiv.org/hep-th/0401187

Berti, Cardoso, Yoshida
"Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation"
http://arxiv.org/gr-qc/0401052

Setare is in Iran, Vagenas at Barcelona.
Berti is in St. Louis, Cardosoo and Yoshida are in Portugal.

Here is the link for this post:
https://www.physicsforums.com/showthread.php?s=&postid=140731#post140731

 

[selfAdjoint]

Didn't Lubos write or cowrite a paper on this subject? I seem to remember it being mentioned some months ago on s.p.r.

 

[marcus]

Originally posted by selfAdjoint
Didn't Lubos write or cowrite a paper on this subject? I seem to remember it being mentioned some months ago on s.p.r.

Sure did. One solo and one with Andy Neitzke that I know of.
would you like the links?

why don't I give them in any case:
Lubos' paper:
http://arxiv.org/gr-qc/0212096

Lubos and Andy's paper:
http://arxiv.org/hep-th/0301173

------------------------

what's exciting about the more recent paper by Gour and Suneeta
is that they challenge the Area operator spectrum derived by Rovelli and Smolin in 1994 and propose a quantum correction in the area.

this resolves a long-standing difficulty and produces some nice
results.

Meteor brought the paper in. I've been reading it and like it quite a bit. (it is however "revisionist" in a sense)

afterthought edit: selfAdjoint, I put a longer discussion of the LQG area spectrum in the thread called "Loop Quantum Gravity". Didnt want to take extra space in this thread which is serving as a link-basket.

 

[marcus]

Program for the May LoopFoam Conference

A couple of days ago Rovelli posted the program for the May 2004 Conference (at Luminy on the Mediterranean)

the organizers:
Laurent Freidel
Philippe Roche
Carlo Rovelli



----exerpted material in no particular order----

A tentative list of morning speakers, still to be confirmed, is as
follows

Loops:
Abhay Ashtekar (quantum geometry)
Thomas Thiemann (dynamics and low energy)
Lee Smolin (overall results)
Ted Jacobson (devil's advocate)

Applications:
Martin Bojowald (loop cosmology)
Alejandro Corichi (black holes)
Daniel Sudarsky (phenomenology)

Spin foams:
John Baez (spinfoams)
Laurent Freidel (GFT, sum over complexes)
John Barrett (BC model)
Alejandro Perez (spinfoams)

Related approaches:
Jorge Pullin (consistent discretization)
Peter Forcacs or Max Neidermair (fixed point)
Ian Ambjorn or Renate Loll (dynamical triangulations)
John Klauder (general covariant dynamics)

...
...

6. SCIENTIFIC PROGRAM

Aim of the conference is to make the point on where we are in the
loop/spinfoam approach to quantum gravity. In particular:
evaluate the results obtained so far, point out open problems,
and discuss the directions of development that appear to be most
promising. The conference is therefore mostly (but not
exclusively) addressed to our community. The four days will
focus on 1) Loops, 2) Applications, 3) Spinfoams, 4) Related
approaches.

The conference will be articulated in:
- morning talks of approximately 30 minutes, meant to summarize the
present state of the different aspects of the field, followed by
ample discussion time.
- afternoon presentations of novel results. The duration of
these will be decided dividing the available time by the
number of communications accepted.
- A panel session, followed by a general discussion, on the last
day.

----end of exerpts----

Philippe Roche at the University of Montpellier has this webpage about the conference:
http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/

Other conferences: Here are some recent and upcoming ones mentioned in a previous post in this thread.

...
...

-------recent conferences------

Strings meet Loops (Albert Einstein Institute, MPI-Potsdam) October 2003
http://www.aei-potsdam.mpg.de/events/stringloop.html

Loop Gravity Workshop (Mexico City) January 2004
http://www.nuclecu.unam.mx/~corichi/lqg.htm

International Conference on Gravity and Cosmology (India) January 2004
http://www.cusat.ac.in/icgc04/

Quantum Gravity Phenomenology, (40th annual Polish Winterschool in Theoretical Physics) February 2004
http://www.ws2004.ift.uni.wroc.pl/html.html

--------upcoming conferences--------


Loop/SpinFoam Conference (Marseille) May 2004
http://www.maths.qmul.ac.uk/wbin/GRnews/conference?03Aug.1
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?10

General Relativity Conference (Dublin) July 2004
more annoucements at
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?conference

...
...

 

[meteor]

"Big crunch avoidance in k=1 loop quantum cosmology"
http://arxiv.org/abs/gr-qc/0312110
Authors: Parampreet Singh, Alexey Toporensky
Abstract:
"It is well known that a closed universe with a minimally coupled massive scalar field always collapses to a singularity unless the initial conditions are extremely fine tuned. We show that the corrections to the equations of motion for the massive scalar field, given by loop quantum gravity in high curvature regime, always lead to a bounce independently of the initial conditions. In contrast to the previous works in loop quantum cosmology, we note that the singularity can be avoided even at the semi-classical level of effective dynamical equations with quantum modifications, without using a discrete quantum evolution"



k refers to curvature. In the case k=1 it represents a flat universe. In the text there's discussion about the geometrical density operator (never heard of this operator before). The effective Friedmann equation for LQC is presented, also the Raychaudhuri equation

 

[marcus]

Originally posted by meteor
"Big crunch avoidance in k=1 loop quantum cosmology"
http://arxiv.org/abs/gr-qc/0312110
Authors: Parampreet Singh, Alexey Toporensky


k refers to curvature. In the case k=1 it represents a flat universe. In the text there's discussion about the geometrical density operator (never heard of this operator before). The effective Friedmann equation for LQC is presented, also the Raychaudhuri equation

Meteor, Bojowald recently gave a survey and cited this article. It was a plenary talk on loop quantum cosmology at a January 5-10
conference called "ICGC 2004"
So he must think it is a good paper. I have not read it. I think the flat case is k=0 and the k=1 case is positive curvature----which would normally lead to a big crunch (at least in the sort of ordinary cosmology we used to have before there was a cosmological constant)

Bojowald's survey talk at the conference is online at arxiv and it has links to lots of recent LQC papers which saves us trouble in that department. One link for many:
Bojowald
Loop Quantum Cosmology: Recent Progress
http://arxiv.org/gr-qc/0402053

 

[marcus]

Phenomenology Conference going on now

There is an event going on now (Feb 4-14) in Poland
about Quantum Gravity Phenomenology
Here is the latest speaker list I could find:
--------quote from program-------
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


...to gather together world-leading scientists working on the field of quantum gravity, astrophysics, and cosmology along with a number of post-graduate students and young post-docs and to offer young scientists the opportunity to learn about recent developments in the theoretical investigation of Planck-scale physics that might be tested experimentally in the near future. The lectures presented at the School would provide a broad coverage of subjects relevant for this field, including models of the fate of Lorentz invariance in quantum space-time, loop quantum gravity and string theory, cosmology and astrophysics.
-----------end quote----------

 

[marcus]

the so-called "Bohr compactification" of the real line
is named after Harald Bohr (b.1877, Niels younger bro)

Hans Halvorson at Princeton is a quality mathematician-cum-philosopher and I like the way he writes. he seems to think philosophically about quantum mechanics but also do functional analysis and topology as well. don't know any more about him.

"Complementarity of representations in quantum mechanics"
http://arxiv.org/quant-ph/0110102

AFAIK no one here has already noted Halvorson or this paper.

The Bohr compactification is important to cosmology and not much is on line about it, but Halvorson's paper is online, and see bottom of page 9, around equation (11) for a brief discussion

**************************

To see how the Bohr compactification fits into quantum cosmology see

Viqar Husain and Oliver Winkler
"On singularity resolution in quantum gravity"
http://arxiv.org/gr-qc/0312094

Best kind of confirmation of Bojowald's work because derives similar results (removal of BB singularity) entirely outside of the Loop Gravity framework.

Bohr compactification enters at top of page 6, right after they introduce the almost periodic functions on the Reals:

"It is well-known that AP(R) is naturally isomorphic to C(R_Bohr), the algebra of continuous functions on the so-called Bohr-compactification of R. As the name suggests, R_Bohr is a compact group which can be obtained as the dual group of R_discr, the real line endowed with the discrete topology. This suggests that taking
L²(R_Bohr,dµ₀),
where µ₀ is Haar measure on R_Bohr, as the
Hilbert space for our theory is a viable option. This is the decisive point where we depart from the traditional approach in geometrodynamics, where the Hilbert space is the conventional Schroedinger space L²(R, dx). Once we adopt this new choice, basis states in our Hilbert space are..."

they don't use the Ashtekar variables! they don't use the connection! they use the same ADM variables that Wheeler and DeWitt tried to use!
but they still manage to remove the Big Bang singularity.
the key thing turns out not to be cooking down LQG to get LQC
but something about an idea Harald Bohr had about "almost periodic functions" and something about topology.

Like what they say on page 10:

"Our main result is that there is an alternative to the Schroedinger quantization of the FRW cosmology in the standard ADM geometrodynamical variables. This quantization leads to conclusions
qualitatively similar to those obtained in loop quantum cosmology starting from the connection triad variables: (i) the Hamiltonian constraint acts like a difference operator, and (ii) the inverse scale factor can be represented as a densely defined operator.

Thus it is the representation space and the realizations of the basic observables rather than the nature of the classical variables that are responsible for the similar conclusions for this model."

their italics, my bolding

thanks to Ranyart for calling Viqar Husain/Oliver Winkler's paper to my attention.

 

[marcus]

Two recent DSR papers

Two new papers were just posted on Doubly Special Relativity

http://arxiv.org/gr-qc/0402092
Giovanni Amelino-Camelia
"Some encouraging and some cautionary remarks on Double Special Relativity in Quantum Gravity"
dated 22 February

(based on a talk given at the 10th Marcel Grossmann meeting on GR)

http://arxiv.org/hep-th/0402117
Jerzy Lukierski
"Relation between quantum kappa-Poincare framework and Doubly Special Relativity"
dated 18 February

 

[marcus]

Jose Mourao has co-authored numerously with such folk as Ashtekar, Lewandowski, Marolf, Thiemann, Renate Loll, and was thesis advisor of Jose Manuel Velhinho

here is a picture of Mourao and some bio stuff
http://www.math.ist.utl.pt/~jmourao/textojm.html

Velhinho's work on disertation with Mourao covered 1995-2001

This looks to me like a good new paper by Velhinho
http://arxiv.org/math-ph/0402060
It presents a summary of how the development of LQG is going
and the style is efficient, not cumbersome. He writes as
a mathematician.

On page 19 is treated the issue of spatial diff invariance---which was the basis of the "nonstandardness" discussion with Urs and others in the TT Loop-String thread, or so I gather from Urs' recent posts.
it is an interesting issue and Velhinho provides a concise overview in a couple of pages.

Velhinho is at University of Beira in Portugal
Murao is in the Mathematics Department at Lisbon Tech (the Inst. Sup. Tech)

 

[marcus]

LQG connects with semiclassical study of black holes
(through the BH entropy formula, Hawking radiation and QN modes)
Here are two interesting papers about Hawking radiation
(predicting that it is not perfectly thermal when quantum effects are adjusted for, and describing the mechanism)

Frank Wilczek and Maulik Parikh
"Hawking Radiation as Tunneling"
http://arxiv.org/hep-th/9907001

Maulik Parikh
"Energy Conservation and Hawking Radiation"
http://arxiv.org/hep-th/0402166
6 pages, dated 23 February

 

[meteor]

"Dynamics of loop quantum gravity and spin foam models in three dimensions":
http://arxiv.org/abs/gr-qc/0402112
Authors: Karim Noui, Alejandro Perez
Abstract:

"We present a rigorous regularization of Rovellis's generalized projection operator in canonical 2+1 gravity. This work establishes a clear-cut connection between loop quantum gravity and the spin foam approach in this simplified setting. The point of view adopted here provides a new perspective to tackle the problem of dynamics in the physically relevant
3+1 case."

I just printed it out :)

 

[ranyart]

Originally posted by meteor
"Dynamics of loop quantum gravity and spin foam models in three dimensions":
http://arxiv.org/abs/gr-qc/0402112
Authors: Karim Noui, Alejandro Perez
Abstract:

"We present a rigorous regularization of Rovellis's generalized projection operator in canonical 2+1 gravity. This work establishes a clear-cut connection between loop quantum gravity and the spin foam approach in this simplified setting. The point of view adopted here provides a new perspective to tackle the problem of dynamics in the physically relevant
3+1 case."

I just printed it out :)

Likewise here, but are you aware there are a number of other compatable papers? all preceeding and very relevant:

http://uk.arxiv.org/abs/gr-qc/0402110

http://uk.arxiv.org/abs/gr-qc/0402111

http://uk.arxiv.org/abs/gr-qc/0402112

http://uk.arxiv.org/PS_cache/gr-qc/pdf/0402/0402113.pdf


Just as an after thought I believe this can go here to?

http://uk.arxiv.org/abs/hep-th/0311030

Or maybe Marcus can place it into a relevant forum?

 

[selfAdjoint]

Working through their paper gr-qc/0402112, I see that Noui and Perez do a standard quantization, regulating to get a finite sum and then showing that the regulator can be eliminated in quantizing. They then show that their physical Hilbert space is the same as the one obtained in the LQG approach.

All of this depends crucially on the fact that they can represent their 2+1 geometry as the product of a Riemann surface and a line. It's not clear how, or if, this quantization could be extended to 3+1 spacetime. On the other hand, the fact that in this case the standard type of quantization agrees with the Ashtekar et al quantization is supportive for the LQG folks.

 

[marcus]

Updating the Surrogate Sticky

We are now at page 11 of the thread, so I will update things and bring the earlier links forward. So far there is no sticky thread for Loop Gravity reference links, and this thread is serving as a surrogate sticky "reference library". Thanks to all who have contributed so far!

-------Loop Gravity texts--------
Rovelli posted the 30 December 2003 draft of his book "Quantum Gravity", to be published this year by Cambridge University Press.
The PDF file is at his homepage
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
The book is around 350 pages long and takes a few (like ten?) minutes to download and convert.
To download the 30 December 2003 draft of the book directly:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Here are Thiemann's Lecture Notes (they have been published in Berlin by Springer Verlag)
"Lectures on Loop Quantum Gravity".
A draft is online at
http://arxiv.org/gr-qc/0210094


-------Quantum Gravity Phenomenology and DSR---------

some recent phenomenology and DSR papers:

Giovanni Amelino-Camelia
"A perspective on quantum gravity phenomenology"
http://www.arxiv.org/abs/gr-qc/0402009
dated 2 February 2004

Giovanni Amelino-Camelia, Jerzy Kowalski-Glikman, Gianlucca Mandanici, and Andrea Procaccini
"Phenomenology of Doubly Special Relativity"
http://arxiv.org/gr-qc/0312124
dated 30 December 2003

Jerzy Kowalski-Glikman
"Doubly Special Relativity and quantum gravity phenomenology"
http://arxiv.org/hep-th/0312140
dated 12 December 2003

Jerzy Lukierski
"Relation between quantum κ-Poincare framework and doubly special relativity"
http://arxiv.org./hep-th/0402117
dated 18 February 2004

other less recent ones:

Jerzy Kowalski-Glikman and Sebastian Nowak
"Doubly Special Relativity and de Sitter space"
http://arxiv.org/hep-th/0304101
dated 11 October 2003

M. Daszkiewicz, K. Imilkowska, J. Kowalski-Glikman
"Velocity of particles in Doubly Special Relativity"
http://arxiv.org/hep-th/0304027
dated 3 April 2003


---------Loop Quantum Cosmology-------

Martin Bojowald
"Loop Quantum Cosmology: Recent Progress"
http://arxiv.org/gr-qc/0402053
One of the invited plenary talks at the January 2004 ICGC
conference (see list of recent conferences)


Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology and Boundary Proposals"
http://arxiv.org/gr-qc/0312103
dated 23 December 2003

Martin Bojowald
"Quantum Gravity and the Big Bang"
http://arxiv.org./astro-ph/0309478
dated 17 September 2003, briefly summarizes how
LQG can serve to cure the big bang singularity and
motivate inflationary expansion. Short and less technical
than the other two papers.

Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology, Boundary Proposals, and Inflation"
http://arxiv.org/gr-qc/0303072
dated 19 March 2003

Shinji Tsujikawa, Parampreet Singh, Roy Maartens
"Loop quantum gravity effects on inflation and the CMB"
http://arxiv.org/astro-ph/0311015
from the Tsujikawa/Singh/Maartens abstract:
"In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early kinetic-dominated super-inflation phase, with a quantum-corrected Friedmann equation. As a result, an inflaton field is driven up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyze the cosmological perturbations and show that loop quantum effects can leave a signature on the largest scales in the CMB, with some loss of power and running of the spectral index."

Viqar Husain and Oliver Winkler "On singularity resolution in quantum gravity"
http://arxiv.org/gr-qc/0312094
this is especially interesting because they duplicate LQC results (for example by Bojowald) using the older version of quantum gravity, ADM variables, quantized metric. Shows that the removal of the big bang singularity is "robust"---doesnt depend on using a particular formalism.

as a background reference for classical (non-quantum) cosmology:
Charles Lineweaver
"Inflation and the Cosmic Microwave Background"
http://arxiv.org/astro-ph/0305179
dated 12 May 2003

-------recent conferences------

Strings meet Loops (Albert Einstein Institute, MPI-Potsdam) October 2003
http://www.aei-potsdam.mpg.de/events/stringloop.html

Loop Gravity Workshop (Mexico City) January 2004
http://www.nuclecu.unam.mx/~corichi/lqg.htm

International Conference on Gravity and Cosmology (India) January 2004
http://www.cusat.ac.in/icgc04/

Quantum Gravity Phenomenology, (40th annual Polish Winterschool in Theoretical Physics) February 2004
http://www.ws2004.ift.uni.wroc.pl/html.html

--------upcoming conferences--------

Loop/SpinFoam Conference (Marseille) May 2004
http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/

http://www.maths.qmul.ac.uk/wbin/GRnews/conference?03Aug.1
http://www.maths.qmul.ac.uk/wbin/GRnews/conference?04Feb.2
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?10

General Relativity Conference (Dublin) July 2004
more annoucements at
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?conference

----------fundamental constants, Planck units, time-keeping-------

Historical source for Planck units, the 1899 paper (thanks arivero!)
http://www.bbaw.de/bibliothek/digital/struktur/10-sitz/1899-1/jpg-0600/00000494.htm

In December 2003, the National Institute of Standards and Technology (NIST) posted new CODATA recommended values for the basic Planck units

http://physics.nist.gov/cuu/Constants/

choose "universal" from the menu to find (among other things) the recommended values of
planck mass
planck length
planck time
planck temperature

A 1997 article on timekeeping, discussing GR effects allowed-for in the GPS
http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf

------observational means for testing quantum gravity------

Floyd Stecker
"Cosmic Physics: the High Energy Frontier
http://arxiv.org/astro-ph/0309027
dated September 2003

Stecker discusses the various earth-based and orbital instruments, currently operating, or under construction, or planned, or proposed, and the kind of data becoming available. Among many other things he discusses GLAST, planned to start operating 2007, which, if there are tiny energy-dependent differences in speed among gamma-ray-burst photons, may be able to detect same. Also discusses neutrino observation.


------links to an unselective assortment of current work------
Livine's thesis
http://arxiv.org/gr-qc/0309028

Girelli and Livine
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

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

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

Velhinho "On the structure of the space of generalized connections"
http://arxiv.org/math-ph/0402060

Noui and Perez "Three dimensional loop quantum gravity: physical scalar product and spin foam models"
http://arxiv.org/gr-qc/0402110

Noui and Perez "Three dimensional loop quantum gravity: coupling to point particles"
http://arxiv.org/gr-qc/0402111

Noui and Perez "Dynamics of Loop Quantum Gravity and Spin Foam Models in Three Dimensions"
http://arxiv.org/gr-qc/0402112

Noui and Perez "Observability and Geometry in Three Dimensional Quantum Gravity"
http://arxiv.org/gr-qc/0402113

Freidel and Louapre "Ponzano-Regge model revisited, I."
http://arxiv.org/hep-th/0401076

Gambini and Pullin "Canonical Quantum Gravity..."
http://arxiv.org/gr-qc/0402062

Buffenoir, Henneaux, Noui, Roche
Hamiltonian Analysis of Plebanski Theory
http://arxiv.org./gr-qc/0404041
(spin foam, BF)


========
simply to have this link on LaTex handy:
https://www.physicsforums.com/misc/howtolatex.pdf

 

[meteor]

"Separable Hilbert space in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0403047
By Carlo Rovelli and Winston Fairbairn

Abstract:"We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot-space of the equivalence classes of graphs under diffeomorphisms is noncountable. However, the continuous moduli labeling these classes do not appear to affect the physics of the theory. We investigate the possibility that these moduli could be only the consequence of a poor choice in the fine-tuning of the mathematical setting. We show that by simply choosing a minor extension of the functional class of the classical fields and coordinates, the moduli disappear, the knot classes become countable, and the kinematical Hilbert space of loop quantum gravity becomes separable"

 

[marcus]

The Spring 2004 issue of Jorge Pullin's newsletter is out.

"Matters of Gravity"
http://arxiv.org./abs/gr-qc/0403051

It has a number of QG conference reports
by Bojowald
Date
Corichi
and others

 

[selfAdjoint]

Thank you Marcus, for pointing to this. John Baez used to keep us up to date on this important publication, but he seems to have moved out of QG. The reports were very interesting.

 

[meteor]

"The Duel: Strings versus loops"
http://arxiv.org/abs/physics/0403112