BFL Ward's Resummed QG: Renormalizable Theory & Cosmological Constant

[erkokite]

Anyone have any thoughts on BFL Ward's work? He claims to have found a perturbatively renormalizable QG theory by using a resummation method. By treating the cosmological constant as a coupling constant, he was able to derive its observed value (or very close to it). There are connections to the Asymsafe models.

Anyone have any thoughts on this?

 

[Demystifier]

Can you give a link to the paper?

 

[marcus]

Can you give a link to the paper?

I think the main paper (which he headlined in a Perimeter conference presentation) is:
http://arxiv.org/abs/hep-ph/0204102
Quantum Corrections to Newton's Law
B.F.L. Ward (1 and 2) ((1) Werner-Heisenberg-Institut, Max-Planck-Institut fuer Physik, Muenchen, Germany, (2) Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee, USA)

We present a new approach to quantum gravity starting from Feynman's formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation techniques already well-tested in other problems. Phenomenological consequences for Newton's law are described. 7 pages, 1 figure; published Mod.Phys.Lett. A17 (2002) 2371-2382

This has been cited 7 times by others in the literature, plus 18 citations by Ward himself, for a total of 25. Here's a video of him explaining his ideas at Perimeter conference in November 2009.
http://pirsa.org/09110043/
Asymptotic Safety and Resummed Quantum Gravity
Speaker(s): B.F.L. Ward
Abstract: In Weinberg’s asymptotic safety approach to quantum gravity, one has a finite dimensional critical surface for a UV stable fixed point to generate a theory of quantum gravity with a finite number of physical parameters. The task is to demonstrate how this fixed point behavior actually arises. We argue that, in a recently formulated extension of Feynman’s original formulation of the theory, which we have called resummed quantum gravity, we recover this fixed-point UV behavior from an exact re-arrangement of the respective perturbative series. We argue that the results we obtain are consistent both with the exact field space Wilsonian renormalization group results of Reuter and Bonanno and with recent Hopf-algebraic Dyson-Schwinger renormalization theory results of Kreimer. We calculate the first "first principles" predictions of the respective dimensionless gravitational and cosmological constants and argue that they support the Planck scale cosmology advocated by Bonanno and Reuter as well. Comments on the prospects for actually predicting the currently observed value of the cosmological constant are also given.
Date: 05/11/2009 - 4:30 pm
Collection: Asymptotic Safety-30 Years After

On page 4 of the Perimeter slides he says he has a new approach and refers only to the 2002 paper of his published in Modern Physics Letters A17 page 2371
"We showed that resummation cures the UV problems of Einstein's theory."
This is the main citation he gives to his own work in this 2009 presentation.

However, towards the end of the presentation, around slide 34, he gives two arxiv numbers:
http://arxiv.org/abs/0808.3124
http://arxiv.org/abs/hep-ph/0607198
These are related to cosmology or a secondary issue, not his central message, but they would have citations to earlier work.
[Yes, 0808.3124 cites "[10] B.F.L. Ward, Mod. Phys. Lett. A17 (2002) 237; Mod. Phys. Lett. A19 (2004) 14; J. Cos. Astropart. Phys.0402 (2004) 011; hep-ph/0605054, hep-ph/0503189,0502104, hep-ph/0411050, 0411049, 0410273 and references therein."]

If I wanted a representative account, I would check out the 2002 paper that serves as the main reference in this conference talk.
(Or watch a few minutes of the video. The questions from the audience start at minute 48, ten minutes from the end. I thought I heard Steven Weinberg put in a comment or two.)

 

[erkokite]

Another important paper:

An Estimate of Λin Resummed Quantum Gravity in the Context of Asymptotic Safety
B.F.L. Ward (1) ((1) Department of Physics, Baylor University, Waco, TX, USA)
(Submitted on 5 Aug 2010 (v1), last revised 18 Oct 2010 (this version, v3))

We show that, by using recently developed exact resummation techniques based on the extension of the methods of Yennie, Frautschi and Suura to Feynman's formulation of Einstein's theory, we get quantum field theoretic descriptions for the UV fixed-point behaviors of the dimensionless gravitational and cosmological constants postulated by Weinberg. Connecting our work to the attendant phenomenological asymptotic safety analysis of Planck scale cosmology by Bonanno and Reuter, we predict the value of the cosmological constant \Lambda. We find the encouraging estimate \rho_\Lambda\equiv \frac{\Lambda}{8\pi G_N} \simeq (2.400\times 10^{-3}eV)^4.

http://arxiv.org/abs/1008.1046"

 

[marcus]

He gives the measured value of rho_Lambda as around
(0.002368 eV)⁴

which makes his own theoretical estimate surprisingly close.

I tried parsing that with the Google calculator to get more conventional units. I am used to thinking of rho_Lambda, the cosmo constant as energy density, as around 0.6 nanojoules per cubic meter.

So I put his figure into google window
0.002368^4 *(1 eV)^4 *(hbar*c)^-3
and indeed it did come out about right: 0.656 nanoPascal or 0.656 nanojoule per cubic meter.

0.002368^4 *(1 eV)^4 is what he said using particle physics vernacular and then I tacked on
(hbar*c)^-3 to make the units come out right (he would think of that as one.)

The source he quotes giving the observed value of the cosmo constant does not give it that way. It gives rho_Lambda as a fraction of the critical density, as I recall. Omega_Lambda.

So to convert that to some other energy density units you have to assume and insert a value for the cosmologists estimate of critical density. When that is not made explicit it can get confusing.

His theoretical Lambda value is not the same as what he said in 2009. As I recall in 2009 it was much smaller than the observed, now, in 2011 it is virtually identical to the observed. It seems almost too good to be true.