Covariant LQG

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  • #2
selfAdjoint
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Hah! I'll have to look at it. The claims in the abstract seem very persuasive. Livine isn't usually off base, either.
 
  • #3
f-h
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What I've heard says it's promising but more incomplete from a technical PoV. IIRC there's no well defined Hilbertspace or Loop transform or anything like the usual technical apparatus. You can't do LOST style quantization with it.

Most people these days work on Spinfoams anyways, for precisely the reasons that Lorentzian LQG would be more attractive (as Livine says this is closely related to BC Spinfoams...)
 
  • #4
marcus
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f-h, have you heard any reaction to the two-part Randono paper that just appeared? (sorry for the off-topic question, but am eager to get some word on it)
 
  • #5
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What I've heard says it's promising but more incomplete from a technical PoV. IIRC there's no well defined Hilbertspace or Loop transform or anything like the usual technical apparatus. You can't do LOST style quantization with it.

Most people these days work on Spinfoams anyways, for precisely the reasons that Lorentzian LQG would be more attractive (as Livine says this is closely related to BC Spinfoams...)

Just reading the first part of the paper, it seems that covariant LQG is the familiar case of trading a theory that is "bad" in some theoretical sense bu sweet to calculate in, with one that is "purer" but tough to get numbers in. Cue the theme music for AQFT.

Working with spin foams as if LQG didn't exists doesn't eliminate the Immirzi problem, and the fact that CLQG has spin foams as its quantum states should suggest some motivations for pursuing it. But note that as Livine states, after several years of work it is still limited to kinematic physics, because nobody can figure out how to make dynamics work with the noncommutative inner product.
 
  • #6
marcus
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Major new CLQG paper

http://arxiv.org/abs/gr-qc/0612071
Plebanski Theory and Covariant Canonical Formulation
Sergei Alexandrov, Eric Buffenoir, Philippe Roche
18 pages

"We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed."

Alexandrov got his PhD in Paris around 2003 and went to Utrecht, now he seems to have moved to Montpellier.
Alexandrov has been the main pusher for CLQG. He has collaborated some with Etera Livine and, IIRC, Freidel.

Roche was the co-organizer with Carlo Rovelli of the Loops '04 conference at Marseille.
Roche and Buffenoir have both been at Montpellier for a long time and have collaborated a lot, IIRC. They have impressed me as smart and especially sharp mathematically. Karim Noui was a young collaborator with them for a while and then went to Penn State. Having Alexandrov collaborate with Roche and Buffenoir on CLQG seems to me to put it on the map in a new way----it establishes the probable importance of CLQG.

(Which the people on this PF thread seemed to have suspected already :smile: )

============================

BTW Kirill Krasnov recently posted a paper employing the Plebanski formulation. Here is something about it
https://www.physicsforums.com/showpost.php?p=1177248&postcount=544
there is a video in the Perimeter archive PIRSA #06110041
and there is a preprint
http://arxiv.org/abs/hep-th/0611182
Renormalizable Non-Metric Quantum Gravity?

Here is the abstract. I think it is the same abstract for the video seminar talk and for the preprint:

"We argue that four-dimensional quantum gravity may be essentially renormalizable provided one
relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general
relativity in which the metric (tetrad), the connection as well as the curvature are all independent
variables and the usual relations among these quantities are only on-shell. One of the Euler-Lagrange
equations of this theory guarantees its metricity. We show that quantum corrections generate a
counterterm that destroys this metricity property, and that there are no other counterterms, at
least at the one-loop level. There is a new coupling constant that controls the non-metric character
of the theory. Its beta-function can be computed and is negative, which shows that the non-metricity
becomes important in the infra red. The new IR-relevant term in the action is akin to a curvature
dependent cosmological 'constant' and may provide a mechanism for naturally small 'dark energy'."
 
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