# If I choose an ordering prescription for one function, do I have to stick to that?

As I checked in my last question here, something like "normal ordering" always goes hand in hand with the definition of an operatorvalued function on the space of operators, like (for example) the hamilton operator, or the electromagnetic field strengh tensor. If I choose, for example for my hamiltonian, such an prescription, like "normal ordering", do I have to stick to it with all other operators that I define? Let my hamiltonian be $:\int E^2 + B^2: = \Sigma_k \omega_k a^\dagger_k a_k$

Does that I mean that the number operator $a^\dagger_k a_k$ and the "uncertainty-operator" $\Delta N^2 = :(a^\dagger_k a_k - \langle N \rangle)^2:$ do also have to be normal ordered?

Of course there's a requirement that in the classical limit the theory agrees with its classical counterpart, but generally this poses no restriction on operator ordering, since all relevant commutators are proportional to $\hbar$ and thus vanish in the classical limit.