Convergence of Perturbation Expansions in Cutoff Meson Theories

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Abstract
It is proved that the perturbation expansion of matrix elements for a class of meson theories has a nonzero radius of convergence. Included are theories which describe bosons of nonvanishing mass, coupled linearly or bilinearly to fermions (but not antifermions) via an interaction which cuts off or attenuates sufficiently rapidly for high boson momenta. By bounding the propagators by their values for zero boson momentum one obtains a majorizing series to the perturbation expansion which converges geometrically.

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