On the Cohomological Structure of Supersymmetric Lagrangeans With and Without Auxiliary Fields

The origin of non-renormalization theorems in field theories with global supersymmetry can be traced to the fact that supersymmetric actions can be viewed as the highest components of respective supermultiplets. Supersymmetric interactions in particular can therefore be represented as supersymmetry variations of lower dimensional field polynomials. We investigate here this algebraic structure in the context of the Wess-Zumino model and N=1 and N=2 supersymmetric Yang-Mills theories.