I am reading something about Kaluza Klein theories and compactification. I have some conceptual question:

(1) Why do we call the fifth scalar field $\Phi$ the dilation field? Is there any scaling property for that?

(2) What happens to this field after dimensional reduction?

Many thanks if you can provide me with further reading material! :)

I am reading something about Kaluza Klein theories and compactification. I have some conceptual question:

(1) Why do we call the fifth scalar field $\Phi$ the dilation field? Is there any scaling property for that?

(2) What happens to this field after dimensional reduction?

Many thanks if you can provide me with further reading material! :)