the future of LQG

julian

In the book "Approaches to quantum gravity" edited by Oriti on page 332 Crane asks Thiemann the question about foliations and Thiemann replies:

"...LQG starts from this classical framework and so one may think it cannot deal with topology change. However, very beautifully this is not the case: vectors in the LQG Hilbert space are superpositions of spin network states. These describe polymerlike excitations of the gravitational field on finite graphs. Consider the volume operator of LQG associated with some spatial region. If that region has empty intersection with the given graph then the volume vanishes. Physically this means that the given state assigns no volume to that region, i.e. that there is a hole in that hypersurface. Hence we see that topology change is all over the place in LQG...."

I think what Thiemann is saying is quite subtle.

julian

Hello tom

I have a limited knowledge of the issues of differentiable structure of spatial diffs in LQG. I know that if the valence of the nodes is great enougth that using the smooth diff structure makes the Hilbert space non-seperable (http://arxiv.org/pdf/gr-qc/0403047.pdf):


"Indeed, as we show below, the nodes of sufficiently high valence have a surprising “rigidity” under smooth transformation, and this rigidity turns out to be the one responsible for the moduli. Therefore the non-separability of [itex]H_{diff}[/itex] is a bizarre remnant of the initial choice of the smooth category. It is therefore natural to explore the possibility of using a slightly different functional class of fields to start with."


I know in the LOST theorem that they consider piecwise analytic structures. This is to avoid the union of two graphs having an infinite number of edges (if piecewise analytic curves intersect at least a countable number of times they will coincide everywhere) - it is crucial that they be piecwise becuase otherwise everything would be determined by the data in an arbitrarily small region (analyticity) and there would be no local degrees of freedom.

I'd be interested to hear more about what you think about the whole issue. Maybe you are right about topology change and diff structure in LQG. Was this not part of the motivation for Thiemann's Algebriac quantum gravity where there is no fumdamental topology or differential structure?

julian

What did ever happen to Markopoulou's approach to renormalisation via Kreimer Hopf algebras? (http://arxiv.org/pdf/hep-th/0006199.pdf). It was such a nice idea.

tom.stoer

I am not sure whether we talk about the same issue. Thiemann asks for topology change, but I am asking for same topology with non-diffeomorphic smoothness structures.

tom.stoer

@marcus, right, we are talking about different time scales regarding "future of LQG".

regarding our everlasting debate on spin networks vs. foams, constraints and anomalous quantization etc.: I think this is the central point simply b/c this the only area of research where I think LQG as of today can be provable wrong (mathematically).

marcus

I'm glad you agree about the timescale difference. We could do a lot better debate-wise if we got clear about basic terms.
I gather from something you said in the "Reformulation" thread that you thought I was thinking "spin networks VERSUS foams".
For me there is no conflict. Each are a necessary part of the theory. Both are purely combinatorial objects. No manifold is needed to define either one. Manifold is extra baggage (in both cases) and out the window. :-)

Basically I try to stay up to date with the majority of the Loop community and adjust my terminology accordingly, so less liklihood for confusion, as I see it.

audioloop

but rovelli base a lot from them (and neglecting time)

Lorentz covariance of loop quantum gravity
http://arxiv.org/pdf/1012.1739v3.pdf

...The possibility of a Lorenz covariant formulations of spin networks has been extensively studied by Alexandrov in [12–14], where several of of the results presented here can be already found....
...See also [31]...


[12–14]
The new vertices and canonical quantization
http://arxiv.org/pdf/1004.2260.pdf

[31]
Towards Loop Quantum Gravity without the time gauge.
http://arxiv.org/pdf/0811.1916.pdf

marcus

The future of LQG is an interesting topic. In his original post (later edited) Julian quoted Ashtekar's overview of the Loop program and then asked "what do you think is the most important direction?"
I replied by highlighting selected parts of the long Ashtekar passage in Julian's original post.

It's a question that we should ask periodically. One thing to note that has bearing on the LQG future is that next year's conference has begun to take shape. The normally biennial Loops conference in effect defines the field and gives a snapshot of the current status of the Loops research program. We should reflect on the people who have joined the Loops 2013 international Advisory Committee. They constitute an interesting assortment.

http://www.perimeterinstitute.ca/en/...s_13/Loops_13/

International Advisory Committee

Giovanni Ameliano-Camelia, University of Rome
Abhay Ashtekar, Pennsylvania State University
Fernando Barbero, Instituto de Estructura de la Materia
John Barrett, University of Nottingham
James Bjorken, SLAC
Martin Bojowald, Pennsylvania State University
Robert Brandenberger, McGill University
Alejandro Corichi, Pennsylvania State University
Fay Dowker, Imperial College, London
Rodolfo Gambini, Instituto de Fisica Facultad de Ciendias
Steve Giddings, University of California, Santa Barbara
Viqar Husain, University of New Brunswick
Ted Jacobson, University of Maryland
Kirill Krasnov, University of Nottingham
Jerzy Lewandowski, University of Warsaw
Stefano Liberati, SISSA
Etera Livine, Ens de Lyon
Renate Loll, Universiteit Utrecht
Joao Magueijo, Imperial College, London
Alex Maloney, McGill University
Matilde Marcolli, California Institute of Technology
Guillermo Mena, Instituto de Estructura de la Materia
Djordje Minic, Virginia Tech
Daniele Oriti, Albert Einstein Institute
Roberto Percacci, SISSA
Alejandro Perez, Centre de Physique Theorique
Jorge Pullin, Lousiana State University
Martin Reuter, Johannes Gutenberg Universitat
Vincent Rivasseau, Laboratoire de Physique Théorique d'Orsay
Carlo Rovelli, Centre de Physique Theorique
Thomas Thiemann, Institut für Theoretische Physik III
William Unruh, University of British Columbia

To make the mix visual, I colored different areas of expertise:
Loop, not colored
Competing QG theories orange (Spectral Geometry, AsymSafe, CDT, CausalSets...)
QG phenomenology (both concrete and speculative) green,
String magenta
with blue for uncategorized all-purpose great people.

16 primarily loop research (with interrelated spinfoam, spinnorial versions, GFT, TQFT)
6 specializing in other QG programs (spectral, asymsafe, triangulations, causal sets)
3 primarily phenomenology---ideas (both solid and speculative) related to testing.
4 string
3 uncategorized blue
Totaling 32, so just about half are drawn from what is usually considered Loop community.

marcus

Another pointer to the future of LQG is the paper which Ashtekar et al just posted on arxiv.
http://arxiv.org/abs/1209.1609
A Quantum Gravity Extension of the Inflationary Scenario
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 7 Sep 2012)
Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This pre-inflationary dynamics also opens a small window for novel effects, e.g. a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early universe.
4 pages, 2 figures

This is one of a number of papers that have appeared in the last 2 years all moving in a similar direction. Early universe phenomenology is one of the (perhaps the single strongest) determinants of the immediate future of LQG. A bunch of research effort uncovering features one could look for in the Cosmic Microwave Background. Often related to inflation--both usual inflation and Loops own type of faster-than-exponential inflation that occurs naturally (without inflaton field) as a result of the bounce. A substantial part of the Loops 2013 conference is almost certainly going to be about this sector of Loop research. So that is one window on the future of LQG (the thread topic) right there.

audioloop

After seeing some articles of the cited researchers, I saw an alternative to the propositions of the inflationary models, written by Magueijo, is nice to see alternatives to the inflationary models

http://arxiv.org/pdf/gr-qc/0007036v1.pdf
...The varying speed of light (VSL) theory provides an elegant solution to the cosmological problems - the horizon,flatness, and Lambda problems of Big-Bang cosmology...


http://arxiv.org/pdf/astro-ph/0305457v3.pdf
...brought a varying speed of light (VSL) into the arenas of cosmology, quantum gravity...



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