How Does Quantum Probability Affect Discrete Space in Loop Quantum Gravity?

[Eh]

I'm wondering how the discrete space in LQG is effected when it becomes a quantum field. In any given volume, you normally could find a continuous amount of intersecting field lines. In LQG, those lines or loops) are discrete, and space is basically a lattice of sorts. So in that case, there would be no continuous space. But what happens when the wave function is added in?

Since these loops do not comprise a static background in which matter and energy move about, and are dynamic, any change in energy with a given volume will necessarily change the local geometry. Since the distribution of energy can only be seen in terms of probability, I'm thinking that the geometry of the network of loops could also only be seen in terms of probability. So while space would be discrete from a classic viewpoint, the wave function itself would be continuous.

Is this the case?

 

[jeff]

Firstly, loop quantum gravity IS a quantum theory of geometry (Did you not know that the "Q" in LQG stands for "quantum"?). Secondly, space in LQG is topologically continuous, only it's geometrical properties like volume or area are discrete. For example, topologically, a sphere in LQG is just an ordinary sphere. However, the spectrum of possible values of it's area is discrete.

 

[Eh]

Yes, I know it's a quantum theory. I was just wondering how probability would effect a classic concept of volumes in a lattice. In other words, within a given volume, is there still an infinite number of possible states for the loops to be in?

I'm not very familiar with the workings of quantum field theory, so my question may seem a little vague or off the mark.