Weil Algebras and Supersymmetry

Abstract

We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are the auxiliary fields. The general N=1 supermultiplet is interpreted in terms of Weil algebras. As specific examples we consider supersymmetric quantum mechanics, Wess-Zumino model and supersymmetric Yang-Mills theory in four dimensions. Some comments on the formulation of constrained systems and integrable models and non-Abelian localization are given.