Abstract
We consider the ϕ4 theory in Euclidean space of complex dimensionv and prove that, for Rev < 4 the renormalized Feynman amplitudes grow at worst exponentially in the number of vertices in the graph. This implies that the Borel transform of any Schwinger function may be defined in a neighborhood of the origin in the Borel plane.
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Communicated by R. Stora
Research partially supported by National Science Foundation, Grant Number Phy 77-02277 A 01
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Rivasseau, V., Speer, E. The borel transform in Euclidean ϕ v 4 local existence for Rev < 4. Commun.Math. Phys. 72, 293–302 (1980). https://doi.org/10.1007/BF01197553
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DOI: https://doi.org/10.1007/BF01197553