Symmetry Invariance, Anticommutativity and Nilpotency in BRST Approach to QED: Superfield Formalism

We provide the geometrical interpretation for the Becchi-Rouet-Stora-Tyutin(BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four$(3+1)$-dimensional ($4$D) interacting U(1) gauge theory within the of superfield approach to BRST formalism. This interacting theory, there is an explicit coupling between the U(1) gauge field and matter(Dirac) fields, is considered on a $(4,2)$-dimensional supermanifold by the four spacetime variables x\μ(\μ=0,1,2,3) and a pair Grassmannian variables \θ and \\θ (with\θ²=\\θ²=0, \θ\\θ+\\θ\θ=0). We the Lagrangian density and (anti-)BRST charges in the language of the and show that (i) the (anti-)BRST invariance of the $4$D Lagrangian is equivalent to the translation of the super Lagrangian density along Grassmannian direction(s) (\θ and/or \\θ) of the$(4,2)$-dimensional supermanifold such that the outcome of the above(s) is zero, and (ii) the anticommutativity and nilpotency of the(anti-)BRST charges are the automatic consequences of our superfield.