The Nature of the Axioms of Relativistic Quantum Field Theory. II

This paper continues the study of the nature and interdependence of the axioms of relativistic field theory; attention is focused on the notion of relativistic invariance. The central result of the present paper is the derivation of necessary and sufficient conditions for a representation of the covariant free field to admit a unitary representation of the inhomogeneous Lorentz group associated with the field operator. It is shown that only the standard Fock-Cook representation has this property. The relevance of the requirement that the Lorentz group is represented by a unitary family associated with the field operator is exhibited by an analysis of the covariant representations of Shale and Segal. These representations involve extremal states which are not pure, and group representations by intertwining operators.