Nilpotent symmetry invariance in the superfield formalism: the 1-form (non-)Abelian gauge theories

We capture the well-known off-shell as well as the on-shell nilpotent BecchiRouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance(s) of the Lagrangian densities of the four (3 + 1)-dimensional (4D) 1-form (non-)Abelian gauge theories within the framework of the superfield formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance(s), and (ii) the above Lagrangian densities, in the language of the specific quantities defined within the above superfield approach to BRST formalism. Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the above superfield formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four spacetime coordinates x (with μ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and θ̄. One of the key results of our present investigation is a great deal of simplification in the understanding of the nilpotent (anti-)BRST symmetry invariance(s) of the above 4D 1-form (non-)Abelian gauge theories within the above superfield formulation where the geometrical interpretations of the above invariance(s) become quite clear. PACS numbers: 11.15.-q, 12.20.-m, 03.70.+k