Abstract
We bound rigorously the large order behaviour of φ 44 euclidean perturbative quantum field theory, as the simplest example of renormalizable, but non-super-renormalizable theory. The needed methods are developed to take into account the structure of renormalization, which plays a crucial role in the estimates. As a main thorem, it is shown that the Schwinger functions at ordern are bounded byK n n!, which implies a finite radius of convergence for the Borel transform of the perturbation series.
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Communicated by R. Stora
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de Calan, C., Rivasseau, V. Local existence of the Borel transform in Euclidean φ 44 . Commun.Math. Phys. 82, 69–100 (1981). https://doi.org/10.1007/BF01206946
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DOI: https://doi.org/10.1007/BF01206946