Superfield Approach To Nilpotent Symmetries For QED With A Single Restriction On Supermanifold

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 ((\bar C)C) and the Dirac fields (\psi, \bar\psi) 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 \bar\theta parametrize this six dimensional supermanifold. The new gauge invariant restriction on the above supermanifold, due to the augmented superfield formalism, owes its origin to the (super) covariant derivatives and their intimate relation with the (super) 2-form curvatures (\tilde F^{(2)})F^{(2)} constructed from the (super) 1-form gauge connections (\tilde A^{(1)})A^{(1)}. The results obtained separately 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 six (4 + 2)-dimensional supermanifold