Arbitrary spin fields: spectral representations for the two-point functions, and the connection between spin and statistics

Abstract

Two-point Wightman functions of arbitrary finite component relaticistic fields (which may in general be reducible under the homogeneous Lorentz group) are related to those involving auxiliary fields transforming according to representations of the type D(j, 0), and explicit representations are obtained on the basis of the usual axioms. Our construction does not require the choice of any special kind of basis for the physical states. Using the spectral representations and the weak local commutativity condition a general proof is given for the spin-statistics connection. Special problems which arise in the case of reducible fields are discussed.