On the decomposition of wightman functionals in the euclidean framework

Abstract

We consider Wightman functionals having the property that the Schwinger functions can be represented by a Euclidean invariant measure on the space of tempered distributions. The strong form of the Osterwalder-Schrader positivity condition is shown to imply that the measure is positive and some restrictions on the Schwinger functions are discussed which guarantee that this condition holds. The ergodic decomposition of the measure leads to a decomposition of the Wightman functional into such with cluster property. We discuss also the role of the positivity condition in connection with a general criterion for the existence of a decomposition.