By P. Urban (auth.), Prof. Dr. Paul Urban (eds.)
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Additional info for Current Problems in Elementary Particle and Mathematical Physics
In summary, we see that it is possible sent the Wightman theory by an integr~l t~ repre- representation upon going to the euclidean region and then requiring a topological property (t-continuity) for the non-coincident Schwinger functions Sn' The nature of the singularities for these functions at coincident arguments is given in  and will not be reproduced here. For an integral representation with only positive measures it is necessary and sufficient to imposes useful conditions on the non-coincident Schwinger functions and what if any regularity properties are forced on the Wightman distributions.
CHALLIFOUR ZiF, University of Bielefeld Germany and Depts. of Mathematics and Physics ++ Indiana University Bloomington, USA 1. INTRODUCTION It is an understatement to say that the last ten years of constructive field theory have brought about a revolution in our understanding of relativistic quantum fields. Even though the models studied so far have been + Lecture given at XV. Internationale Universitatswochen fUr Kernphysik,Schladming,Austria,February 16-27,1976. ++Permanent address. 46 super-renormalizable they have provided not only new techniques but a new conceptual framework which unifies quantum fields and statistical mechanics.
Streit, W. Wyss, unpublished. 18. Discussions with V. Enss were very helpful in clarifying this point. 19. C. Hegerfeldt, Contribution to the ZiF-Symposium Dec. 75, and K. C. Hegerfeldt, Is the Wick Square Infinitely Divisible 7, ZiF preprint,1976. 20. C. Hegerfeldt, Corom. Math. Phys. 45, 133 (1975). 21. K. Osterwalder and R. Seneor, The S-Matrix is Nontrivial for Weakly Coupled P(~)2 Models, preprint 1975. P. Eckmann and J. ), ZiF-Symposium Sept. 1975, to appear (Springer, Vienna + New York) .