How do you explkain the difference of labels and dynamical variable?

[kof9595995]

I think I understand this, but when I tried to explain it to a friend I couldn't phrase it in a nice and clear way. How would you guys explain it to others?

 

[Pengwuino]

I don't understand what you even mean. You need more context I think.

 

[kof9595995]

Like in fluid theory, Eulerian coordinate is (sort of?) labels and Lagrangian coordinate is dynamical variables?
Or in old quantum mechanics, when treating EM interation with particle, we write the field as $A(\hat {x})$, where $\hat {x}$ denote the position observable of the particle(so it's a dynamical varible), whereas in QFT we write the field as $\hat{A}(x)$ where x is just a spatial coordinate(a label),as said in http://press.princeton.edu/chapters/s7573.pdf : In quantum field theory, x is a label, not a dynamical variable. The x appearing in ϕ(t, x) corresponds to the label a in qa(t) in quantum mechanics. ...

 

[kof9595995]

Emm, it's a bit hard to even express my question clearly, but I'll give it a try: say position x, in order to specify a partcle's postion, which is a dynamical variable(DM for short), we must have a coordinate system, which has all possible values of x, and this coordinate system works like labels, so is it correct to say in order to define a position as a DM it's inevitable to define position labels first? Or is DM is a "subconcept" of coordinate labels?...
I realize my question is ambiguious, please bear with me...