Going Beyond LQG: how to define QFT over Loops?

[marcus]

... die in ignorance or lqg (wan yidun's nick on this forum) or anyone else will have to help me! Oh damn, I feel awful. And Marcus hates me now.

You should be applying your intelligence to unimodular QG. That is where things are happening right now.

This is just the advice of an attentive bystander, but I will give it to you anyway (even though you haven't asked and probably don't want advice.)

LQG already has a way to carry matter and has had for some time. The important goal now is simply to handle quantum geometry itself with only token generic matter.

Unimodular addresses not only the cosmoconstant, which everybody thinks is so important. (After all it is 75 percent of the universe ) Unimodular addresses something much more basic---the awkward fact that until now the LQG Hamiltonian is a constraint.
It addresses what has been a major barrier or hurdle, a "sticking point", if you know the expression.

This unimodular gambit might fail, and disappoint expectations, but I don't think anyone can predict the outcome at this junction. If it does not fail then it "turns the tables".

You should watch the PIRSA seminar talk about it, which goes farther than the recent paper.
http://pirsa.org/09050091/

It turns out that there is a variable that is canonically conjugate to the cosmoconstant. This variable is related to time in a curious way. Integrating it over the present tells you the volume of the past. Also if you have a network representing the geometry of the present there is a natural way to divide up the volume of the past and assign a certain amount to each node of the network. Each node in the network has an accumulation of time that builds up there. In a sense, evolution is proceeding independently everywhere, at every node, and there is a collective evolution, a collective time, which is the sum of all the separate fingers or branches of evolution. It is a surprisingly beautiful variation on General Relativity---which already Weinberg was talking about in 1989 but he did not go forward with it (it seems to need something like the spin network to carry out the quantization of Unimodular Relativity and Weinberg didn't have tools to quantize so he stopped short.)

Ultimately, this could be the answer to your question "QFT over Spin Networks".
They already have a formalism to define QFT over Spin Networks, what is needed is to get the networks oiled so they work properly.

 

[MTd2]

I get it now the meaning of why Spin Networks:

This is the mathematical formulation of Rovelli's Relational Quantum Mechanics.

Please, help me! Otherwise I will become an EMO!

 

[marcus]

I'm not sure what to say about spin networks, and this perception of them as embodiment of a relational approach.
There is the idea that reality could be described minimally as pure abstract relation. Geometric relations, material relations to geometry. In my mind it is very vague. I don't feel sure enough about any of this to talk about it.

BTW Rovelli has a new paper recalling some previous work with Krasnov in which the center of a black hole is treated as a spin network node with many many links coming out of it. Could this be a useful description? Would it contribute to correctly computing the entropy? I don't know.

In Smolin's new paper the global time is the volume of the past. From the seminar talk, one sees that the present is described by a spin network and, curiously enough, the nodes of the network turn out to share the past. Each network node is assigned a share of the volume, in what appears to be a natural way. This seems very strange.

 

[Max™]

Why should it seem strange? After all measured time is defined locally, not globally.

Picture your location as the top of a hill, as you look in any direction, you're looking "downhill" in time.

Smolin is a strong believer that the GR picture of time is correct, he's simply placing each node so it views itself at the top of the hill, and thus has it's own unique contribution to any slice you claim as the present.

You can't apply the time labels to all the nodes in a general fashion because you lose connection with SR/GR in the time definition (implying a distinguishable sense of simultaneity).

I like LQG, a lot, but their bottom up method is too... complex and fractured I fear, more likely to produce useful results than Strings... but I think it will be an odd evolution from their model that produces anything like reality, if anything.