Some remarks about the localization of states in a quantum field theory

For the case of a field theory with a nuclear space of test functions (for instance, the space of strongly decreasing test functions) compact sets of states are constructed; these correspond to sets of localized states. Only such states are considered which are elements of a fixed subspace of the entire Hilbert space. This subspace belongs to them-point functions of order less than a certain fixed 2n.Supported in part by the Air Force Office of Scientific Research under Grant AF 500–64On leave of absence from the Max Planck-Institut für Physik und Astrophysik, München.