Is the ground state in LQG a coherent state?

In summary, there is currently a lot of discussion and research happening around the topic of coherent states in LQG. Coherent states are being considered as a possible way to correspond classical spacetimes in LQG, and there are different approaches being explored in the literature. Some researchers are particularly impressed with the work of Bianchi et al, who have proposed coherent states in the holomorphic representation and have also addressed issues related to semiclassical states. There is also an interesting idea that coherent states in LQG could be stable against decoherence from interactions with matter, similar to how coherent states in quantum optics are stable against interactions with the environment.
  • #1
atyy
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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?
 
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  • #2
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.
 
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  • #3
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
 
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  • #4
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.
 
  • #5
Demystifier said:
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
 

1. What is the ground state in LQG?

The ground state in LQG refers to the lowest energy state of the quantum system, also known as the vacuum state. In Loop Quantum Gravity (LQG), this is a discrete state of the gravitational field, which is described by a network of intersecting loops.

2. What is a coherent state in LQG?

A coherent state in LQG is a quantum state that describes a superposition of many loop states, and is often considered to be a semiclassical state. It is characterized by having a well-defined classical geometry, and is used to describe the gravitational field in LQG.

3. How is the ground state related to coherent states in LQG?

In LQG, the ground state is considered to be a coherent state, as it represents the lowest energy state of the quantum system. However, it is important to note that the ground state is not a unique coherent state, as there are many different coherent states that can describe the same gravitational field in LQG.

4. How is the ground state in LQG determined?

The ground state in LQG is determined through a process called state-sum construction, which involves summing over all possible states of the gravitational field. This includes both loop states and coherent states. The ground state is then identified as the state with the lowest energy in this sum.

5. What is the significance of the ground state in LQG?

The ground state in LQG is significant because it represents the lowest energy state of the gravitational field, and is used as a starting point for calculating other physical quantities in LQG. It also plays a crucial role in understanding the quantum nature of the gravitational field and its relation to classical geometry.

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