Nonperturbative construction of nonrenormalizable models of quantum field theory in four-dimensional space-time

The report presents the construction of non-cutoff Euclidean Green's functions for nonrenormalizable interactions _I()= d(ge): exp : in four-dimensional space-time. It is shown that all axioms for the generating functional of E.G.F. are satisfied except perhaps theSO(4) invariance. It is shown that the singularities of E.G.F. for coinciding points are not worse than those of the free theory.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.Supported in part by NSF Grant No INT 73-20002 A 01 (formerly GF-41958).The author would like to thank Professors T.Balaban, J.Fröhlich and A.Uhlmann for interesting discussions and valuable suggestions. He would also like to express his sincere thanks to Professor J.Niederle for the very kind hospitality extended to him during his stay at the Symposium on Mathematical Methods in the Theory of Elementary Particles in Liblice Castle.