My level is not sufficient enough to easily understand QFT yet there is some basic question I need to understand in it - what in QFT corresponds to a wave function in QM, for a single particle case and, say, for a more general case of multiparticle nonseparable state (suppose the particles are identical). I do understand Fock space idea as well as creation-annihilation operators idea, yet I cannot grasp what is that operator field considered in QFT and how it may correspond to the general multiparticle case of QM. If this field defines an operator at each space point, then on which vector space does it act and how it may be related to the multiple particle wave function? Or maybe it is not the operator field itself which corresponds in QFT to the wave function/particles state, but something else? I tried to look through some discussions here and on other sites but did not succeed to see or grasp what is the solution. Thank you.