On some nonunitary representations of the Poincaré group and their use for the construction of free quantum fields

Abstract

In this paper a class of nonunitary infinite dimensional Hilbert space representations of a semidirect product is investigated. The equivalence of this category with the category of finite dimensional representations of the stability subgroups is shown. This theory is applied to the Poincaré group and to the construction of free quantum fields. In an appendix a method is introduced for building an infinite family of finite dimensional indecomposable representations of the noncompact Euclidean group in two dimensions. Such representations are used for carrying out the analysis of the massless fields.