  In the framework of superfield approach, we derive the local, covariant,
continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry
transformations on the U(1) gauge field $(A_\mu)$ and the (anti-)ghost fields
$((\bar C)C)$ of the Lagrangian density of the two $(1 + 1)$-dimensional QED by
exploiting the (dual-)horizontality conditions defined on the four $(2 +
2)$-dimensional supermanifold. The long-standing problem of the derivation of
the above symmetry transformations for the matter (Dirac) fields $(\bar\psi,
\psi)$ in the framework of superfield formulation is resolved by a new set of
restrictions on the $(2 + 2)$-dimensional supermanifold. These new physically
interesting restrictions on the supermanifold owe their origin to the
invariance of conserved currents of the theory. The geometrical interpretation
for all the above transformations is provided in the framework of superfield
formalism.
