Covariant fields: poincarè group representations and metric structure in the space of quantum states

Abstract

The representations of the Poincarè group realized over the space of covariant fields transforming according to any irreducible representation D^(m,n) of the Lorentz group are constructed explicitly with reference to a helicity basis.he representation is indecomposable in the massless case. The form of this representation together with the invariance of two-point Wightman functions of the field (which follows from a weak set of axioms) determines the metric tructure in the space of quantum states of the field. This astructureis explicitly determined for general D^(m,n). Certain particular cases (especially the symmetric traceless tensor field) are discussed indetail. Finally we consider the representation pertaining to massive fields, and examine the passage to the limit of vanishing mass. We present a limiting procedure which leads form the unitary representation of the massive field to the indecomposable non-unitary reperesnetation of the massless field.