# Talk:Canonical quantum gravity

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## Several Points

I intend to attempt a reasonably comprehensive rewrite of this article over the next few days. There are a few important reasons why I think that the article needs this:

1) The article opens by stating "In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity." While this is perfectly correct, it's hardly a great first sentence for an article which is ostensibly concerned with canonical gravity.

2) The majority of the article seems to obfuscate the distinction between canonical gravity and the canonical quantisation of gravity (the first half of the article is particularly at fault in this). These are distinct topics, although canonical quantisation of gravity obviously draws heavily on the canonical formulation of gravity.

3) The article probably needs to be renamed. As it currently stands, it is a description of the canonical picture of general relativity. There exist several other theories of gravity which admit straightforward canonical descriptions. Furthermore, physicists who actually work in this area always make a distinction between canonical general relativity and canonical versions of other theories such as Brans-Dicke or relational models. (I have already corrected this.)

4) Although the article begins by talking about canonical quantum gravity, the author apparently quickly lost steam and all mention of this topic has disappeared by the time the article finishes.

5) The references are a mess. The important work on constrained systems is Dirac's, not Bergmann's. Furthermore, the idea that an article on canonical general relativity can succeed without, for example, referencing the original ADM paper is ridiculous.

Given that the talk page for this article is a graveyard, I'm simply going to go ahead and make what I believe to be the necessary changes. I shall spend the next week or two writing an article on paper before uploading it here. Should anyone object, I'd appreciate if we could discuss any further changes or reverts here on the talk page. St Cyrill 02:07, 18 August 2006 (UTC)

I wrote this article, and I agree with the broad thrust of your points. I think you're missing the point that the article is a "stub" (i.e. a sketch or an incomplete article) which you are welcome to expand. Let me say that
2. I don't really understand this point. The article doesn't discuss the quantization. That bit was left out.
3. Fine, but instead of having been renamed it could have been expanded to include those theories.
4. True. It also fails to discuss Hartle-Hawking, which would have been nice, among many other things.
5. Read it again. Dirac's contribution is perfectly clear. ADM wasn't referenced because, in the existing text, there is no occasion to. –Joke 04:07, 27 September 2006 (UTC)

There is no formula in this headword discovered by B. DeWitt. All is work of Dirac and ADM. —Preceding unsigned comment added by 89.103.146.30 (talk) 08:07, 24 February 2008 (UTC)

## Foliation

The article does not mention the foliation of space-time into space and time, in the sense that every manifold is descomposed in the form $(T,M)$ where T is a "time" dimension and M is the spatial part of the Manifold (x,y,z) hence for the Riemann scalar inside the Einstein-Hilbert Lagrangian you have:

$R_{00}+R^(3)$

$R_{00}=T_{00}=\rho$

and $R_{00}$

$R^(3)$

are "energy" densities so when you integrate them respect to the measure $\sqrt-g^(3)$ you get the energy of the system.

## Extrinsic Curvature

I corrected the definition. The partial derivative with time of the 3 metric should be with co-ordinate time t (as it is now) not the proper time \tau as it was before. The factor of the lapse in the definition of the Extrinsic curvature ensures this is not co-ordinate dependent, e.g. in the case of zero shift K_ij = 1/2 dt/d\tau d\gamma_it/dt.

## Brans-Dicke Theory?

I would like to see an extension of this approach to include a scalar field in the Lagrangian density. —Preceding unsigned comment added by 12.169.97.130 (talk) 18:55, 9 July 2010 (UTC)

## Total derivatives?

I agree with the previous comment that the decomposition of the metric tensor is based on the ADM formalism. Why not mention it? In particular, you mention particular total derivatives being eliminated. I gather that these correspond to surface terms but it would be nice to have a few words explaining the justification for their elimination. Are these derivatives, the ones shown in the re-formulated Lagrangian (density) from ADM? Is it that you expect flat-space in the far field? Or is it simply that you are happy with the Euler-Lagrange equations as they are? TonyMath (talk) 21:45, 6 March 2012 (UTC)

## Problems with Opening, Missing Details

Point 1: The first sentence reads "In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity)."

But I would like to suggest that canonical quantum gravity is an attempt using some canonical formulation of general relativity. For example, we have the ADM formalism but we also have Ashtekar variables.

Point 2: The second sentence reads "It is a Hamiltonian formulation of Einstein's general theory of relativity."

This is not quite accurate! Classical canonical gravity indeed is some Hamiltonian formulation of general relativity...but canonical quantum gravity takes one particular Hamiltonian formulation, then quantizes it canonically.

Point 3: The commutation relations are missing!

There is no discussion of the surface deformation algebra, the commutation algebra of the (smeared) constraints, the relation to the Diffeomorphism group, etc. This is bad! The Bergmann-Komar group should be discussed somewhere!

Maybe these are trivialities, but I think perhaps a more historical approach should be taken as Rovelli's "Notes for a brief history of quantum gravity" (arXiv:gr-qc/0006061) does... --Pqnelson (talk) 16:03, 21 September 2012 (UTC)