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The combined supersymmetric and gauge-invariant field theories are formulated using ordinary fields, not superfields, from the start, thereby eliminating reference to superfluous components. The construction is a generalization to supersymmetry of the minimal-coupling procedure of ordinary gauge theories. The Lagrangians obtained coincide with those of the superfield approach in the Wess-Zumino gauge. The Ward-Takahashi identities of Green's functions for fields and supersymmetry currents are obtained by functional methods. The Ward-Takahashi identities are presented in a form from which low-energy theorems for Goldstone fermions can be directly derived, and the proof of the Goldstone theorem in these combined theories is clarified. Discussion of the closure of the supersymmetry algebra leads to the concept of gauge-invariant translations for which the conserved current is a gravitational energy-momentum tensor. Some of the results are valid in a broader context than supersymmetry and are applicable to gauge theories in general.
Wit et al. (Wed,) studied this question.