speaking of creation and annihilation operators. I want to ask this since days ago. In every point of the quantum fields, are there creation and annihilation operators that is in addition to the say spin or momentum operators or are creation, annihilations, spin, momentum operators can only be used one point of the field at a time? For example, one point of the field lower and rise particle by creation and annihilation operators.. while in another point of the field, it's spin operator acting on the state, while in another, it's momentum operator acting on the state.. or does the same momentum operator also have creation annihilation in *same* point of the field?They are different things - the fields and the states its operates on.
The mathematical connection is it can be shown the field is the same as creation and annihilation operators.