Creation, annihilation and motion

[Kyleric]

I'd like to know if creation and annihilation operators are involved in a free trajectory of a particle from point A to point B. If it's the case, how so?

If there is a detector at A, and another one at B, mathematically speaking, can it be said that the particle is annihilated at A, and created at B later on ?

 

[Simon Bridge]

Is that how creation and annihilation operators are generally used?
Wouldn't you normally have the particle created at the source and annihilated at the detector?