hi all In Quantum Mechanics, physical states are described by functions defined on space. Through Schrodinger evolution we get functions on space time. In their book “PCT, Spin and Statistics, and All That” the authors write that fields are operator valued distributions on smooth test functions. These test functions are defined on space time. http://en.wikipedia.org/wiki/Wightman_axioms They say that test functions with a support in a laboratory and within 1 second are related to the measures one can do in these conditions. These functions have no "time evolution" constraints Can these test functions represent physical states? And when?