Eur. Phys. J. C (2006) 47: 219-226
https://doi.org/10.1140/epjc/s2006-02542-6

Theoretical Physics

Augmented superfield approach to exact nilpotent symmetries for matter fields in non-Abelian theory

Department of Physics, Banaras Hindu University, Varanasi, 221005, India

^* e-mail: malik@bhu.ac.in

Received: 3 January 2006
Published online: 27 April 2006

Abstract

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^μ (with μ=0,1,2,3) and a couple of Grassmannian variables θ and θ̄. 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 within the framework of augmented superfield formalism.