Analytic Properties of Nonstrictly Localizable Fields

Abstract

A class of test functions ``minimal with respect to causality'' is introduced. The corresponding fields are called local. Tempered and strictly localizable fields are local, but there is a large class of fields that are local but not strictly localizable. For local fields, the analytic properties of vacuum expectation values are studied. The local fields that are not strictly localizable are characterized by an arbitrary fast increase of Wightman functions near the light cone. With an adequate definition of local commutativity, other properties of tempered and strictly localizable fields seem to remain valid.