Unconstrained supersymmetry

Abstract

This is a first step towards better superfield formulations of supersymmetric field theories. The simple Wess-Zumino model (including renormalizable interactions) is formulated in terms of an unconstrained, scalar superfield, obeying a wave equation that includes the square of the super Klein-Gordon operator. This wave equation is derived from an action principle, by unconstrained variation of the superfield. The physical content of the theory is the same as for the original formulation by Wess and Zumino, and the Feynman rules are identical to those of Grisaru, Roček and Siegel. Next, super electrodynamics, including minimal interactions with a scalar matter multiplet, is given a similar treatment. There is no need, in this case, to include higher derivatives in the Lagrangian. The matter field is an unconstrained, scalar superfield, and the gauge fields are also contained in an unconstrained, scalar superfield. The scattering matrix coincides with that of the conventional form of super electrodynamics with Wess-Zumino matter fields. Supersymmetric spinorial currents are found by simple and direct application of the Noetherian method, in superfield language. Conservation laws of the formD _a J ^a=0 (resp.D _a J ^ab=0) are derived from gauge invariance (resp. supersymmetry). Extension to super Yang-Mills theories is straightforward.