Non-renormalization theorems without supergraphs: the Wess-Zumino model

The non-renormalization theorems of chiral vertex functions are derived on the basis of an algebraic analysis. The property, that the interaction vert ex is a second supersymmetry variation of a lower dimensional field monomia l, is used to relate chiral Green functions to superficially convergent Gre en functions by extracting the two supersymmetry variations from an interna l vertex and transforming them to derivatives acting on external legs. The analysis is valid in the massive as well as in the massless model and can b e performed irrespective of properties of the superpotential at vanishing m omentum. (C) 2000 Elsevier Science B.V. All rights reserved.