Overlapping Divergences and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-Matrix

Abstract

By extending considerations given by Dyson, general rules are obtained for isolating divergent parts from integrals corresponding to overlapping graphs, and a proof is obtained for the appearance of an extra factor $Z_{1}^{}{}_{}{}^{\ensuremath{-}1}$ from "$b$ divergences." In the last section the possibility of renormalization for scalar meson-nucleon interactions is demonstrated.