Robert Schrader

Robert Schrader is well known for his fundamental work with K. Osterwalder on the euclidean formulation of quantum field theory. They gave a set of necessary and sufficient conditions for a set of euclidean Green functions to be the analytic continuation to imaginary time of a set of Wightman functions. Their first paper ("Axioms for Euclidean Green's Functions", Commun. Math. Phys., 31, 83-112, 1973) contained a mistake, in that the given conditions on the euclidean functions did not guarantee that the corresponding Wightman functions were tempered. This was corrected in their second paper, ibid, 42, 281-305, 1975; the correct condition turned out to be difficult to use. So in this paper, they also give a set of convenient sufficient conditions on the functions. Most of the models constructed so far obey this larger set of properties. So, whatever was the actual method used to establish the existence of the models originally, it is likely that a euclidean proof of existence would be feasible.