On the Borel summability of planar perturbation series: Transition to Minkowski space

In recent years 't Hooft and Rivasseau proved the Borel summability of planar asymptotically free massive theories in Euclidean space. The corresponding Borel sums in Minkowski space are shown to exist as linear functionals if the Euclidean counterparts are bounded polynomially in momentum space and fulfill certain analyticity conditions. Both can be verified in massive planar wrong sign ₄⁴ using Rivasseau's approach. The functionals alternatively are densely defined and unbounded on anL^p space or bounded on (the whole of) a Banach space with a more restrictive norm.Supported by a scholarship of the NATO scientific committee via the German academic exchange service (DAAD)After October 1, 1987: Max-Planck-Institut für Physik, Föhringer Ring 6, D-8000 München 40, Federal Republic of Germany