Superfield approach to nilpotent symmetries for QED from a single restriction: an alternative to the horizontality condition

We derive together the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin ( BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A mu), the (anti-) ghost fields (( (C) over bar ) C) and the Dirac fields (psi (psi) over bar) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting a single restriction on the six ( 4, 2)dimensional supermanifold. A set of four even spacetime coordinates x(mu) (mu = 0, 1, 2, 3) and two odd Grassmannian variables theta and (theta) over bar parametrize this six-dimensional supermanifold. The new gauge invariant restriction on the above supermanifold owes its origin to the ( super) covariant derivatives and their intimate relations with the (super) 2-form curvatures ((F) over tilde (2)) (F) over tilde (( 2))) F-(2) constructed with the help of 1-form (super) gauge connections ((A) over tilde (1)) (A) over tilde ((1))) A((1)) and (super) exterior derivatives ((d) over tilde )d d) d. The results obtained by exploiting (i) the horizontality condition, and (ii) one of its consistent extensions, are shown to be a simple consequence of this new single restriction on the above supermanifold. Thus, our present endeavour provides an alternative to ( and, in some sense, generalization of) the horizontality condition of the usual superfield formalism applied to the derivation of BRST symmetries.