# A Loop Quantum Gravity question

Can someone answer this question, I have chosen this from Bodendorfer's article on 'An Elementary Introduction to Loop Quantum Gravity' from section 3 General relativity in the connection formulation and quantum kinematics exercise 3.6.10

Ashtekar-Lewandowski Vaccum

A Cylindrical Function Ψ = 1, this state is called Ashtekar-Lewandowski Vacuum. Show that it corresponds to a maximally degenerate Spatial Geometry by evaluating the Vacuum expectation value of the Flux Operator

It's not that hard to see actually. Draw an arbitrary auxiliary graph, and note that the Ashtekar-Lewandowski vacuum state corresponds to a spin network on this graph with all spins equal to zero (because the spin-0 representation of $$SU(2)$$ is the trivial representation that assigns $$1$$ to each of its elements, which leads exactly to the state $$\Psi[A] = 1$$).
Now remember that area in LQG is proportional to $$A \sim \sum \sqrt{j(j+1)}.$$
Substitute $$j = 0$$ and you will get $$A = 0$$ – all areas vanish for such a state. I believe that's what "maximally degenerate spatial geometry" means.