Recent paper: LQG fails to give correct semiclassical limit

[ensabah6]

Sometimes I wonder if LQG is as much of a "failure" as string theory, with string theory inability to dimensionally reduce uniquely, and LQG unable to define hamiltonian constraint.

Recent paper


http://arxiv.org/abs/1005.1866

Large-spin asymptotics of Euclidean LQG flat-space wavefunctions

http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.1866v1.pdf
Aleksandar Mikovic, Marko Vojinovic
(Submitted on 11 May 2010)
We analyze the large-spin asymptotics of a class of spin-network wavefunctions of Euclidean Loop Quantum Gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an amplitude for a spin network whose graph is a composition of the the wavefunction spin network graph with the dual one-complex graph and the tetrahedron graphs for a triangulation of the spatial 3-manifold. This spin-network amplitude can be represented as a product of 6j symbols, which is then used to find the large-spin asymptotics of the wavefunction. By using the Laplace method we show that the large-spin asymptotics is given by a sum of Gaussian functions. However, these Gaussian functions are not of the type which gives the correct graviton propagator.

on page 20 "The asymptotics is not of the type required for correct semiclassical limit"

Perhaps an entirely new approach is needed, one that starts with correct semiclassical limit and work backwords (and whose kinematics, volume and area operators may disagree with LQG)

 

[francesca]

Oh my god ensabah6! This is the second time that you make me jump on my chair: "Damn, I missed that there is a big problem here or there in LQG!" Then, taking a brief look to the papers that you are posting, I realize the following thing: Mikovic and Vojinovic, in a similar manner of Alexandrov in a recent paper (https://www.physicsforums.com/showthread.php?t=395833"), are moving by their on personal assumptions, and then they find that these assumptions don't work and this results in some inconsistency in the theory. This does not mean that Loop Quantum Gravity is inconsistent or fails, this just alerts us that if we want to use these assumptions then we will have a problem. It is good to explore this kind of things: while you are constructing a theory, it's good to know if something is wrong so you can discard it and keep what works.

Going just a bit more in the detail of this particular paper, I have just taken a very brief look to it, but I can see that it does not consider at all some of the most important results of the last few years, like the use of coherent states and the calculation of the asymptotic by the Nottingham group.

I'm sorry that I will not go further in details, I hope that eventually someone else will comment, but I just wanted to post my first reaction.

Francesca

 

[f-h]

I discussed these results with Mikovic a while ago, they are not incompatible with the positive results in the new vertices. It's crucial to understand that he is talking about old fashioned LQG not about the idea to define the dynamics using spin foams.

I don't recall the technical details from the top of my head but the paper is not really concerned with the same theory we looked at:

"One can argue that some other wavefunction may give the correct asymptotics, but the problem is to see what other wavefunction can replace Ψk(Γ,j0). Although our result applies only to the Euclidean LQG, one wonders what is the relevance of this result for the Lorentzian LQG, given that there is a strong belief that the Euclidean and the Lorentzian theories should be related by some kind of an analytic continuation. Note that Lorentzian analogs of the Euclidean wavefunctions used in this paper are not known. However, one can try use one of the recently proposed Lorentzian spin foam models [12, 13, 14] in order to construct a Lorentzian spin-network wavefunction."

The asymptotics of the wave function defined by these spin foam models have been computed and their overlap with coherent kinematical states that are not geometric is exponentially suppressed, and the asymptotic behaviour is of the form that gives the propagator.

That said, Mikovics notion of asymptotic behaviour is conceptually sound. So it's good to try to understand it in some detail.