Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter   Fields In Non-Abelian Theory
  We derive the nilpotent (anti-)BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x^\mu (with \mu = 0,1,2,3) and a couple of Grassmannian variables \theta and \bar{\theta}. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4, 1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed in the framework of augmented superfield formalism. 
R. P. Malik (CAS, Phys. Deptt., BHU) and Bhabani Prasad Mandal   (Banaras Hindu University)