A generalization of the horizontality condition in the superfield approach to nilpotent symmetries for QED with complex scalar fields

We provide a generalization of the horizontality condition of the usual superfield approach to the Becchi - Rouet - Stora - Tyutin ( BRST) formalism to obtain the (anti-) BRST symmetry transformations for all the fields of a four (3 + 1)dimensional interacting 1-formU(1) gauge theory ( QED) within the framework of the augmented superfield formalism. In the above interacting gauge theory, there is an explicit coupling between the 1-form U( 1) gauge field and the complex scalar fields. This interacting gauge field theory is considered on the ( 4, 2)- dimensional supermanifold parametrized by the four even spacetime variables x(mu) (with mu = 0, 1, 2, 3) and a pair of odd Grassmannian variables theta and (theta) over bar. The above nilpotent ( anti-) BRST symmetry transformations are obtained due to the imposition of a gauge (i.e. BRST) invariant restriction on the appropriate superfields defined on the (4, 2)-dimensional supermanifold. This restriction owes its origin to a pair of ( super) covariant derivatives and their intimate connection with the 2-form ( super) curvatures. The results obtained, due to the application of the horizontality condition alone, are contained in the results deduced due to the imposition of the above gauge invariant restriction.