(canonical) quantization of teleparallel gravity

[tom.stoer]

Does anybody know about an attempt to quantize teleparallel gravity?

I would like to learn more about it, canonical approaches preferred: is there a sound formalism to implement the constraints / symmetries? Do we know the physical Hilbert space? Can one construct Dirac observables? Does the construction of energy carry over to the quantized version?

If all this has NOT been done yet - why?

Last question: can one say that Einstein-Cartan-Gravity which is the basis for canonical LQG unifies both GR + teleparallel gravity, therefore the latter one is automatically "contained" in LQG?

 

[marcus]

I hope other people will have some suggestions. I don't know much about teleparallel.
I think you have a good idea to look into it. Aldrovandi and Pereira have argued that working with teleparallel rather than standard general relativity could be the key to getting a good theory of quantum gravity.
Luca Bombelli has a list of links:
http://www.phy.olemiss.edu/~luca/Topics/grav/teleparallel.html

I have the vague idea that somehow teleparallel gravity has a kinship to noncommutative field theory (but this is so vague I probably should not mention it.)

If you don't mind my pasting in some abstracts I will get some stuff. It won't be perfect, just something to start with.

 

[marcus]

I've posted about other Aldrovandi and Pereira papers before. They are reputable Brazilian physicists but they tend to explore some wild ideas (that's good, but they are not typical mainstream.)

Here are the relevant A&P. You may already know these papers! They make a strong case that one should quantize teleparallel as way to get QG.

http://arXiv.org/abs/gr-qc/0509051
General relativity and quantum mechanics are conflicting theories. The seeds of discord are the fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal in the sense that a particle does not follow one trajectory, but infinitely many trajectories, each one with a different probability. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction, while torsion in teleparallel gravity acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principles. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics.
Comments: 15 pages, 2 figures. Talk presented at the conference "Quantum Theory: Reconsideration of Foundations-3", June 6-11, 2005, Vaxjo University, Vaxjo, Sweden

http://arXiv.org/abs/gr-qc/0603122
Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence principle, and is able to provide a tensorial definition for the energy-momentum density of the gravitational field. Considering the conceptual conflict between the local equivalence principle and the nonlocal uncertainty principle, the replacement of general relativity by its teleparallel equivalent can be considered an important step towards a prospective reconciliation between gravitation and quantum mechanics.
Comments: 9 pages. Contribution to the proceedings of the Albert Einstein Century International Conference, Paris, 18-22 July, 2005

I have to go, will look at this some more later.

 

[marcus]

So far I may merely be coming up with sources you already know, or which have only tenuous connection with the topic. Better than nothing, I hope.

Here is a pedagogical introduction to noncommutative field theory, with relations to DSR, quantum gravity, and one reference to a 2001 paper on telelparallel by Szabo and Langmann.

http://arXiv.org/abs/0906.2913
Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
Richard J. Szabo
(Submitted on 16 Jun 2009 (v1), last revised 5 Oct 2009 (this version, v3))
A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what extent noncommutative gauge theories may be regarded as gauge theories of gravity. UV/IR mixing is explained in detail and we describe its relations to renormalization, to gravitational dynamics, and to deformed dispersion relations in models of quantum spacetime of interest in string theory and in doubly special relativity. We also discuss some potential experimental probes of spacetime noncommutativity.
Comments: 26 pages, 4 figures; v2: comments and references added; v3: typos corrected, clarifying comments and references added; Based on Plenary Lecture delivered at the XXIX Encontro Nacional de Fisica de Particulas e Campos, Sao Lourenco, Brasil, September 22-26, 2008; Final version to be published in General Relativity and Gravitation.

My provisional non-expert opinion is that somebody could produce publishable research papers about canonical quantization of teleparallel gravity.

Luca Bombelli is well connected with the QG community (he has organized some international QG conferences set in Corsica). I think he knows who is doing what. A researcher could write to Bombelli and get help with the roadmap.
Then if you got started on it, this paper might help, because it gives a canonical formulation of classical parallel gravity.
A possible place to start:

http://arXiv.org/abs/hep-th/0002022
Hamiltonian structure of the teleparallel formulation of GR
M. Blagojevic, I. A. Nikolic
17 pages, published in Physical Review D62 (2000) 024021
(Submitted on 2 Feb 2000)
"We apply Dirac's Hamiltonian approach to study the canonical structure of the teleparallel form of general relativity without matter fields. It is shown, without any gauge fixing, that the Hamiltonian has the generalized Dirac-ADM form, and constraints satisfy all the consistency requirements. The set of constraints involves some extra first class constraints, which are used to find additional gauge symmetries and clarify the gauge structure of the theory."

 

[tom.stoer]

Thank's a lot. It will take some time to study these papers ...

 

[marcus]

Thank's a lot. It will take some time to study these papers ...

I wish we could get suggestions from some other people. Demystifier, who sometimes posts here, might have very different suggestions. Also Arivero might already know something about teleparallel gravity. I know very little about the topic, not enough to evaluate these papers and say which ones might be worth reading.

 

[tom.stoer]

I had a look at these papers; they are dealing with the classical gauge structure of teleparallel gravity. It is a nice summary, but does not touch quantization at all.

It is clear that a structure that is very similar to gauge theories is easier to quantize than some thing that does not make use of these common concepts - but that applies to Einstein-Cartan-Gravity as well. For me the latter one appears as the most natural theory of gravitation as it uses a more general spacetime structure to construct the theory on top of it - no restrictions like vanishing curvature or torsion.