Is the Kodama state a viable solution for quantum gravity?

[marcus]

I didnt know of Kristin Schleich and Don Witt before. they have coauthored a recent paper with Stephon Alexander (Stanford, SLAC) some of whose previous work has already been discussed here
(here is a list of 19 papers by Alexander http://arxiv.org/find/grp_physics/1/au:+Alexander_S/0/1/0/all/0/1 )

Schleich and Witt papers go back to 1993 at least. Here are 16 by Schleich:
http://arxiv.org/find/grp_physics/1/au:+Schleich_K/0/1/0/all/0/1

BTW it seems they were interested in "dynamical triangulation" (Ambjorn, Jurkiewicz) approach to QG back in 1996

the present paper is about the Kodama state (and is partly directed towards answering Edward Witten's criticisms of it in http://arxiv.org/gr-qc/0306083 )

I see that Kristin is an Associate Professor in the UBC department (vancouver) where Bill Unruh is. Here is a picture
http://www.physics.ubc.ca/php/directory/research/fac-1p.phtml?entnum=149
It looks like Uni British Columbia is another place in North America where a grad student can do nonstring Quantum Gravity research.
UWO (dan christensen), UC Davis, UC Riverside, Uni Waterloo, and of course Penn State are others

 

[marcus]

What is this man smiling about?

http://www.physics.ubc.ca/php/directory/research/fac-1p.phtml?entnum=181


he is probably pretty happy about the Schleich, Witt, Alexander paper

and then, back in 1976 or so, he was the first person to realize that there would be a temperature and thermal radiation simply associated with acceleration, analogous to the hawking temperature and hawking radiation associated with black holes that was derived at about the same time.

the guy is one of a handful of founders of Quantum Gravity as a field

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

the Kodama state could be (is probably, IMO) the "ground state" for gravity with a positive cosmological constant, and it may have the correct classical limit and all that good stuff.

the main obstacle to adopting the Kodama as a kind of vacuum state for LQG seems to be an objection raised by Ed Witten in 2003 to a paper by Smolin where Smolin was proposing to do exactly that.

since 2003 several papers have explored "what might be wrong with Witten's objection to the Kodama state?"

************
I had another look at Bill Unruh snapshot.
wondering what he would say if Witten view of Kodama state turned out in error and this paper by Kristin at the Unruh's UBC department turned out to be the right approach to it.

 

[marcus]

each time I look at this little 4 page paper i get more interested by it.
here are some exerpts:

----from Kristin Schleich et al on Kodama state----
Notably, in contrast to Yang-Mills field theories, the irreducible representations of these equivalence classes of diffeomorphisms not in the identity component need not be one-dimensional for all hypersurface topologies.

Infact, these irreducible representations can carry spin 1/2
[4, 5, 13].
The goals of this paper are to provide a simple derivation of these spin1/2 representations for an interesting classof 3-manifolds and to discuss their relevance to some recent comments about the Kodama state from Witten [6]...

... Note that in this case there is no free parameter as in the case of traditional theta-states in Yang-Mills. One can choose the representation, but having done so, its structure is fixed. Thus the specification of the representation is an essential part of the initial conditions for the quantum state space and once chosen, cannot be tuned by a physical mechanism...
...
These properties of a spinorial Kodama state could potentially change the conclusions of Witten for such 3manifolds. Witten studied the normalizability of the Kodama state for the Abelian and Yang-Mills gauge theories and found that the Hamiltonian constraint admitted both a normalizable and non normalizable part. This can be explicitly be seen, for example, by noting that if one chooses a normalizable Kodama state and acts on it with CP , the state will transform into a unnormalizable Kodama state. This happens because the Chern-Simons functional is CP odd. A Fock space can be constructed from expanding about the Kodama state and one finds that gravitons of one helicity have positive energy and those of the opposite helicity have negative energy. For the spinorial Kodama state, as discussed above, there is no definition of parity. Hence, what is meant by CP for such manifolds is not clear. In particular there will be no map which can reverse the sign of the ChernSimons action and thus interchange Chern-Simons wavefunctions.
---end quote---

 

[marcus]

I see that Kristin has written a Java applet

http://noether.physics.ubc.ca/Sims/explain folder/index.html

that simulates things orbiting a black hole

because of radical precession you don't get the standard ellipse orbit.
I got her program to run. pretty much all you have to do is
push the button labeled "orbitz" and watch, using the suggested default values of the orbit parameters

she and J.Friedman and Donald Witt have also proved a theorem they call
"topological censorship"
[Friedman, J., Schleich, K, Witt, D., "Topological Censorship",
Phys. Rev. Lett., 71, 1486-1490 (1993)]. which is that if the universe is got some screwy topololgy with wormholes then you can't tell because you can't get thru.
so the universe might as well have a simple topology. which is what
I personally thought all along but anyway they proved a theorem which is all to the good---for sure there's no better way than theorems to get the world sorted out

 

[marcus]

what Smolin "Invitation to LQG" says about Kodama

I took a look at Smolin's "Invitation" survey to see what he had to say
and it didnt sound very optimistic. On page 23 he says:

---quote---
24. For the case of non-vanishing cosmological constant, of either sign, there is an exact physical state, called the Kodama state, which is an exact solution to all of the quantum constraint equations, whose semiclassical limit exists[100]. That limit describes deSitter or anti-deSitter spacetime. Solutions obtained by perturbing around this state, in both gravitational[11] and matter fields[101], reproduce, at long wavelength, quantum field theory in curved spacetime and the quantum theory of long wave length, free gravitational waves on deSitter or anti-deSitter spacetime 27. It is not yet known whether or not the Kodama state can be understood in a rigorous setting, as the state is not measurable in the Ashtekar-Lewandowski measure which is an essential element of the rigorous approach to the canonical quantization. At the same tine, the integrals involved are understood rigorously in terms of conformal field theory. ...
---end quote...

but that was back in August 2004, when Smolin wrote the survey
http://arxiv.org/hep-th/0408048

here is another paper by Smolin (with Laurent Freidel) about the Kodama state
http://arxiv.org/abs/hep-th/0310224
The linearization of the Kodama state
Laurent Freidel, Lee Smolin
14 pages
Class.Quant.Grav. 21 (2004) 3831-3844

"We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant."

I wonder if Kristin Schleich et al will make Smolin and Freidel reconsider the conclusions in this paper which are generally unfavorable to the stated conjecture.