Is the ground state in LQG a coherent state?

[atyy]

As I understand, it is postulated that only coherent states in LQG correspond to classical spacetimes. Is the ground state of LQG a coherent state? Otherwise, what principle selects that the universe should be in a coherent state?

 

[marcus]

Area and volume are excitations of geometry. The state with no area and no volume would correspond to a spin network with no nodes and no links, I suppose.

Just guessing. Perhaps you can find a discussion of the ground state of geometry. All I can recall is an off-hand remark in a paper by Ashtekar from some time back where he said essentially what I just did, using the phrase "excitations of geometry".

You ask about coherent states in LQG. That's currently an active topic! Quite a lot of discussion going on in the literature. A recent paper that I've been looking at is December 2009 "Coherent Spin-Networks" by Bianchi Magliaro Perini. There are different approaches to constructing coh. states and they show a degree of convergence among them.

 

[marcus]

Francesca or F-H might have something to say about this. Hopefully Tom.Stoer when he gets back from mountains.

I'll tell you what my intuitive take on it is---LQG is being radically reformulated starting 2008 when the canonical+spinfoam approaches merged. What you have now are various proposals for coherent states.

If I had to bet on some one team's proposals---well that would be unfair to the valuable and innovative work of other good researchers, but if I had to bet---I would say to watch for the papers on this and related topics by Bianchi et al.

Not just about defining the coherent states, but also addressing semiclassical and holomorphic issues.

The reason for that (possibly incorrect) bias is that I am extremely impressed by these two papers by Bianchi et al:

0912.4054 Coherent spin-networks
1004.4550 Spinfoams in the holomorphic representation

 

[Demystifier]

Perhaps one should use an analogy with quantum optics, where coherent states emerge dinamically. It turns out that coherent states are, under certain conditions, stable with respect to decoherence caused by interactions with the environment. In quantum gravity, the role of environment could be played by matter.

 

[marcus]

Perhaps one should use an analogy with quantum optics, where coherent states emerge dinamically. It turns out that coherent states are, under certain conditions, stable with respect to decoherence caused by interactions with the environment. In quantum gravity, the role of environment could be played by matter.

That's an intriguing idea! The coherent states in LQG have recently come into sharper focus. Ideas of coherent, holomorphic, and semiclassical states have converged. Rovelli's April paper (1004.1780) provides a condensed review/status report for LQG as a whole, and he covers this on pages 4 and 5. Section E: "Coherent states and holomorphic representation".

I am discussing the April LQG survey or status report paper in another thread, so to keep the discussion together I won't try to talk about coherent states here. Will just give a link to that thread: the "QG five principles" one.
https://www.physicsforums.com/showthread.php?t=420888