As fields ##\phi ## are ill defined at precise time and position i read that fields have to be smeared. So we have test functions f in bounded regions in space time. We have a Hilbert space and ##\phi (f) ## is an operator which acts on H. Maybe we can retrieved the usual wave function when it acts on the vacuum of H? So we start from a test function defined on a region of spacetime. Does this distribution evolves in time? Have i to write ##\phi (t, f) ## ? If f has a support in a space time domain D,what about the wave function outside of D? I can understand that f is null behind the walls of the lab, before and after the apparatus is switched off. What is the relation to the state vector of the measured observable ? thank you.