Local supersymmetry in superspace

Supersymmetric Yang-Mills and gravitational theories are formulated in terms of connections on superspace. The anticommutator of the spinor components of the connections are constrained. This gives the usual supersymmetric Yang-Mills theory and a formulation of supergravity in terms of a gauge phase factor. Supergauge invariance is used to reduce the phase factor to Wess-Zumino form, leaving the local supersymmetry algebra which agrees with the transformations of Breitenlohner.