Superfield Approach To Exact And Unique Nilpotent Symmetries

Abstract

In the framework of usual superfield approach, we derive 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_μ) and the (anti-)ghost fields ((\bar C)C) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting the horizontality condition defined on the six (4, 2)-dimensional supermanifold. The long-standing problem of the exact derivation of the above nilpotent symmetry transformations for the matter (Dirac) fields (\bar ψ, ψ), in the framework of superfield formulation, is resolved by a new restriction on the (4, 2)-dimensional supermanifold. This new gauge invariant restriction on the supermanifold, due to the augmented superfield formalism, owes its origin to the (super) covariant derivatives. The geometrical interpretations for all the above off-shell nilpotent transformations are provided in the framework of augmented superfield formalism.