The Concept of Nonlocalizable Fields and its Connection with Nonrenormalizable Field Theories

Abstract

From an investigation of the two‐point function in nonrenormalizable field theories, it is shown that at least in certain approximations, a nonrenormalizable field is nonlocalizable. This is intimately connected with the occurrence of essential singularities on the light cone in the Wightman functions of the field. Green's functions cannot be defined and the observables, in particular the scattering matrix elements, have to be expressed directly in terms of the unordered expectations values.