Loop Quantum Gravity and Correspondence Principle

[haushofer]

Hi,

I'm a non-expert on LQG, and have a question about it:

What is the status of the correspondence principle applied to LQG?

I.e., in which sense can we take the classical (h --> 0) or non-relativistic (c --> oo) limit in order to obtain classical GR or Newtonian gravity out of LQG? Any reference are also appreciated :)

 

[marcus]

The graviton propagator shows an inverse-square dependence. The most recent overview of Loop is a set of slides from the talk at Stockholm MG13 in July. I will get the link and indicate which slide has about the inverse-square dependence (essentially recovering Newtonian gravity)

Basically you go to Carlo R's home page http://www.cpt.univ-mrs.fr/~rovelli/
and scroll down to the bottom where it says "Recent talks".
One of these is:
http://www.cpt.univ-mrs.fr/~rovelli/RovelliStockholmSpinFoam.pdf
"Covariant Loop Quantum Gravity:
State of the art, Recent developments, Open problems"

Slide#19 has "The free graviton propagator is recovered" and references to a few papers 2009-2011
The context is important, and is illustrated schematically in the previous slide#18.

*Convergence* presents interesting open problems and this is diagrammed on slide#22:
This is the slide with the heading
"Main open issue: Do radiative corrections destroy the viability of the expansion?"

This is the problem that is getting concentrated attention, discussed in the remainder of the slides, #22-26.
Obviously one can only say the quantization is good if the classical theory is recovered as the continuous limit.

 

[atyy]

EPRL in the large spin and Immirzi zero limit seems to match Regge gravity. Does Regge gravity yield GR?

 

[haushofer]

So GR can be obtained unambigiously from LQG in the classical limit?

I'll take a look at the papers mentioned in Rovelli's talk, thanks for that! :)

 

[atyy]

So GR can be obtained unambigiously from LQG in the classical limit?

I'll take a look at the papers mentioned in Rovelli's talk, thanks for that! :)

Not yet. Try the discussions of http://arxiv.org/abs/1105.0216 and http://arxiv.org/abs/1107.0709 .

 

[marcus]

I wouldn't say the situation is as clear as your words suggest. I mentioned inverse-square dependence of graviton propagator. It is "Newtonian" in that sense.
Atyy mentioned how the theory approximates Regge gravity in a certain limit. That's good but that would be for an arbitrary Regge triangulation. There is still the issue of a limit over all triangulations, under refinement, if that makes sense to you.

Evidence has been piling up that the theory recovers GR, I think it's reasonable to expect that.

However I don't think Rovelli claims that there's a complete proof. In the last 4 slides he emphasizes open problems about convergence.

He tends towards caution and understatement. There's a paper by Warsaw group (Lewandowski) that basically says we have quantum gravity and it's Loop. I have a lot of respect for Lewandowski. I think he is less cautious, but brilliant and highly creative. Maybe that's good. But I feel like waiting until I hear definitely from others. I should get the link.

http://arxiv.org/abs/1009.2445
Gravity quantized
Marcin Domagala, Kristina Giesel, Wojciech Kaminski, Jerzy Lewandowski
(Submitted on 13 Sep 2010 (v1), last revised 10 Oct 2010 (this version, v3))
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom because no symmetry reduction has been performed at the classical level.
18 pages

 

[haushofer]

Ok, thanks for all the replies and papers, I will definitely take a look! I'm more familiar with String Theory, so these LQG papers are often a bit hard to read for me, but I'd like to make a comparison between LQG and ST concerning the correspondence principle.

If I have more questions concerning the papers, I'll come back. Thanks again! :)

 

[atyy]

If EPRL is similar to Regge gravity, and Regge gravity is the starting point for CDT, then EPRL in the large spin limit is like CDT? I guess there are two things in the way of this - first, it doesn't seem to be exactly Regge, and second CDT had this Lorentzian rotation.

However, does the latest CDT paper strike anyone as similar to the latest spin foam large spin limit papers?

Second- and First-Order Phase Transitions in CDT
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory